3.6: Conclusion
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 Businesses expanded in scale and scope. The nature of labor shifted. A middle class rose. Wealth concentrated. Immigrants crowded into the cities, which grew upward and outward. The Jim Crow South stripped away the vestiges of Reconstruction, and New South boosters papered over the scars. Industrialists hunted profits. Evangelists appealed to people’s morals. Consumers lost themselves in new goods and new technologies. Women emerging into new urban spaces embraced new social possibilities. In all of its many facets, by the turn of the twentieth century, the United States had been radically transformed. And the transformations continued to ripple outward into the West and overseas, and inward into radical protest and progressive reforms. For Americans at the twilight of the nineteenth century and the dawn of the twentieth, a bold new world loomed.


6.4: Reading- International Trade Barriers
Trade barriers are government-induced restrictions on international trade, which generally decrease overall economic efficiency.
KEY points
- Trade barriers cause a limited choice of products and, therefore, would force customers to pay higher prices and accept inferior quality.
- Trade barriers generally favor rich countries because these countries tend to set international trade policies and standards.
- Economists generally agree that trade barriers are detrimental and decrease overall economic efficiency, which can be explained by the theory of comparative advantage.
Terms
- Tariff: A system of government-imposed duties levied on imported or exported goods; a list of such duties, or the duties themselves.
- Quota: A restriction on the import of something to a specific quantity.
Examples
Trade barriers are government-induced restrictions on international trade. Man-made trade barriers come in several forms, including:
- Tariffs
- Non-tariff barriers to trade
- Import licenses
- Export licenses
- Import quotas
- Subsidies
- Voluntary Export Restraints
- Local content requirements
- Embargo
- Currency devaluation
- Trade restriction
Most trade barriers work on the same principle–the imposition of some sort of cost on trade that raises the price of the traded products. If two or more nations repeatedly use trade barriers against each other, then a trade war results.
Economists generally agree that trade barriers are detrimental and decrease overall economic efficiency. This can be explained by the theory of comparative advantage. In theory, free trade involves the removal of all such barriers, except perhaps those considered necessary for health or national security. In practice, however, even those countries promoting free trade heavily subsidize certain industries, such as agriculture and steel. Trade barriers are often criticized for the effect they have on the developing world. Because rich-country players set trade policies, goods, such as agricultural products that developing countries are best at producing, face high barriers. Trade barriers, such as taxes on food imports or subsidies for farmers in developed economies, lead to overproduction and dumping on world markets, thus lowering prices and hurting poor-country farmers. Tariffs also tend to be anti-poor, with low rates for raw commodities and high rates for labor-intensive processed goods. The Commitment to Development Index measures the effect that rich country trade policies actually have on the developing world. Another negative aspect of trade barriers is that it would cause a limited choice of products and, therefore, would force customers to pay higher prices and accept inferior quality.
In general, for a given level of protection, quota-like restrictions carry a greater potential for reducing welfare than do tariffs. Tariffs, quotas, and non-tariff barriers lead too few of the economy’s resources being used to produce tradeable goods. An export subsidy can also be used to give an advantage to a domestic producer over a foreign producer. Export subsidies tend to have a particularly strong negative effect because in addition to distorting resource allocation, they reduce the economy’s terms of trade. In contrast to tariffs, export subsidies lead to an over allocation of the economy’s resources to the production of tradeable goods.
International trade barriers can take many forms for any number of reasons. Generally, governments impose barriers to protect domestic industry or to “punish” a trading partner.
GLOSSARY
Agriculture
The art or science of cultivating the ground, including the harvesting of crops, and the rearing and management of livestock; tillage; husbandry; farming.
Comparative advantage
The ability of a party to produce a particular good or service at a lower marginal and opportunity cost over another. The concept that a certain good can be produced more efficiently than others due to a number of factors, including productive skills, climate, natural resource availability, and so forth.
Currency
Money or other items used to facilitate transactions. In economics, currency is a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation’s money supply. Paper money.
Developing
Of a country: becoming economically more mature or advanced; becoming industrialized.
Economy
Collective focus of the study of money, currency and trade, and the efficient use of resources. The system of production and distribution and consumption. The overall measure of a currency system; as the national economy.
Efficiency
The extent to which a resource, such as electricity, is used for the intended purpose; the ratio of useful work to energy expended. The extent to which time is well used for the intended task. Improved efficiency was a principle goal of progressives, one they thought attainable by the application of scientific and rational thought to social problems.
Export
This term export is derived from the conceptual meaning to ship the goods and services out of the port of a country. To sell (goods) to a foreign country. Any good or commodity, transported from one country to another country in a legitimate fashion, typically for use in trade.
Free trade
Free trade is a policy by which a government does not discriminate against imports or interfere with exports by applying tariffs (to imports) or subsidies (to exports) or quotas. International trade free from government interference, especially trade free from tariffs or duties on imports.international trade free from government interference, especially trade free from tariffs or duties on imports
Good
An object produced for market.
Import
Something brought in from an exterior source, especially for sale or trade. To bring (something) in from a foreign country, especially for sale or trade.
Industry
The sector of the economy consisting of large-scale enterprises.
Lead
Potential opportunity for a sale or transaction, a potential customer.
License
The legal terms under which a person is allowed to use a product.
Market
A group of potential customers for one’s product. One of the many varieties of systems, institutions, procedures, social relations and infrastructures whereby parties engage in exchange.
Potential
Currently unrealized ability. A curve describing the situation where the difference in the potential energies of an object in two different positions depends only on those positions.
Price
The price is the amount a customer pays for the product. The quantity of payment or compensation given by one party to another in return for goods or services. The cost required to gain possession of something.
Product
Any tangible or intangible good or service that is a result of a process and that is intended for delivery to a customer or end user. Anything, either tangible or intangible, offered by the firm as a solution to the needs and wants of the consumer; something that is profitable or potentially profitable; goods or a service that meets the requirements of the various governing offices or society.
Resource
Something that one uses to achieve an objective. An example of a resource could be a raw material or an employee. Something that one uses to achieve an objective, e.g. raw materials or personnel.
Resource allocation
Resource allocation is used to assign the available resources in an economic way. It is part of resource management. In project management, resource allocation is the scheduling of activities and the resources required by those activities while taking into consideration both the resource availability and the project time.
Security
The condition of not being threatened, especially physically, psychologically, emotionally, or financially. proof of ownership of stocks, bonds, or other investment instruments.
Standard
Something used as a measure for comparative evaluations. A level of quality or attainment.
Trade war
The practice of nations creating mutual tariffs or similar barriers to trade.
- International Business. Authored by : Boundless. Provided by : Boundless. Located at : https://www.boundless.com/business/ . License : CC BY-SA: Attribution-ShareAlike
- Image of Singapore Port. Authored by : Lukacs. Located at : http://en.Wikipedia.org/wiki/File:SingaporePort1.JPG . License : CC BY-SA: Attribution-ShareAlike


1.7.3: Rethinking Drinking
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Does alcohol impact my calorie intake?
Alcoholic beverages are not a component of the USDA Dietary Patterns and the calories consumed are considered discretionary. Alcohol provides 7 calories per gram consumed, and the ingredients in certain mixed drinks, including soda, mixers, and heavy cream, also can contribute to intake of added sugars and saturated fat. Thus, regular consumption of alcoholic beverages can make it challenging for adults to meet food group and nutrient needs while not consuming excess calories.
Why is being able to “hold your liquor” a concern?
For some people, it takes quite a few drinks to get a buzz or feel relaxed. Often they are unaware that being able to “hold your liquor” isn’t protection from alcohol problems, but instead a reason for caution. They tend to drink more, socialize with people who drink a lot, and develop a tolerance to alcohol. As a result, they have an increased risk for developing alcohol use disorder. The higher alcohol levels can also harm the liver, heart, and brain without the person drinking noticing until it’s too late. And all people who drink need to be aware that even moderate amounts of alcohol can significantly impair driving performance, even when they don’t feel a buzz from drinking.
Why are women’s low-risk limits different from men’s?
Research shows that women start to have alcohol-related problems at lower drinking levels than men do. One reason is that, on average, women weigh less than men. In addition, alcohol disperses in body water, and pound for pound, women have less water in their bodies than men do. So after a man and woman of the same weight drink the same amount of alcohol, the woman’s blood alcohol concentration will tend to be higher, putting her at greater risk for harm.
Isn’t drinking good for the heart?
The short answer is, it is unknown whether light-moderate alcohol consumption has positive health impacts, such as decreasing your risk of cardiovascular disease. Many studies have indicated that moderate alcohol consumption has protective health benefits (e.g., reducing risk of heart disease), and others show this may not be true. Thus, there is not a solid conclusion to this question and it warrants more research.
Can I do anything to protect my liver from the effects of too much alcohol?
There are no guarantees that anything will protect the liver from too much alcohol. Liver damage from heavy drinking happens in stages. Some relatively mild damage may happen after a single binge drinking episode, but this reverses itself if the heavy drinking stops. If heavy drinking continues, however, liver damage can progress through several more advanced stages, and repair becomes much more difficult, if not impossible. When the damage goes as far as cirrhosis, the only treatment is liver transplant. The best way to protect your liver’s health is by staying within the low-risk drinking limits or — if you already have liver damage or any signs of an alcohol problem — by quitting.
Also, it’s best if people who drink avoid acetaminophen [1] (found in Tylenol® and other medications). Even the standard recommended dose of acetaminophen can increase the risk of liver damage, particularly among people who drink heavily.
Quitting or Reducing Drinking
The first step, of course, is to decide whether cutting down or quitting is best for you. If you are thinking about quitting, recognize that one size doesn’t fit all, and it’s important to find options that appeal to you. Changing habits such as smoking, overeating, or drinking too much can take a lot of effort, and you may not succeed with the first try. Setbacks are common, but you learn more each time. Each try brings you closer to your goal. Whatever course you choose, give it a fair trial.
Rethink drinking: Begin by evaluating your own drinking
- Make a list of Pros & Cons : What are your reasons for and against making a change?
- Are you ready to change? See what to do if you’re not quite ready to change your drinking .
- To cut down or to quit … Consider which is best for you.
- Create a Change Plan to help you solidify your goal and how you’ll reach it.
Thinking about cutting back on alcohol?
- Review Tips to Try Cutting Back on Alcohol and select two or three to try in the next week or two. It may help to have reminders to reinforce your decision to make a change, such as automated smartphone alerts that you send yourself.
Support for Quitting Drinking
- You do not need to quit on your own, there is support available to help you!
- Try the NIAAA Alcohol Treatment Navigator. The Navigator helps adults find alcohol treatment for themselves or an adult loved one. The Navigator will steer you toward evidence-based treatment, which applies knowledge gained through decades of carefully designed scientific research. If you are seeking help for a teen, check out these recommended adolescent treatment resources . If you are seeking treatment for yourself, you are taking an important step in your route to recovery. You may wish to ask someone you trust to help you through the process and for support along the way.
-
Evidence-based behavioral treatments, or “talk therapy,” include:
-
Cognitive-behavioral therapy (CBT).
- This form of therapy is focused on identifying the feelings and situations (called “cues”) that lead to heavy drinking, and managing stress that can lead to relapse. The goal is to change the thought processes that lead to alcohol misuse and to develop the skills necessary to cope with everyday situations that might trigger problem drinking.
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Motivational enhancement therapy.
- This therapy focuses on helping the patient identify the pros and cons of seeking treatment, form a plan for making changes in drinking behavior, build confidence, and develop the skills needed to stick to the plan.
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Contingency management approaches.
- This approach is used to reinforce positive behaviors such as abstinence or regular attendance.
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12-Step Facilitation Therapy
- An engagement strategy used in counseling sessions to increase a patient’s active involvement in 12-step-based mutual help groups (such as AA), in addition to professionally-led outpatient treatment. The counselor works with the patient to encourage, review, and reinforce their participation in AA, in a structured process that may include reading assignments, journaling, and setting AA participation goals for the week.
-
Cognitive-behavioral therapy (CBT).


3.2: Heterogeneous Equilibria
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Learning Objectives
- To understand how different phases affect equilibria.
When the products and reactants of an equilibrium reaction form a single phase, whether gas or liquid, the system is a homogeneous equilibrium. In such situations, the concentrations of the reactants and products can vary over a wide range. In contrast, a system whose reactants, products, or both are in more than one phase is a heterogeneous equilibrium, such as the reaction of a gas with a solid or liquid.
As noted in the previous section, the equilibrium constant expression is actually a ratio of activities. To simplify the calculations in general chemistry courses, the activity of each substance in the reaction is often approximated using a ratio of the molarity of a substance compared to the standard state of that substance. For substances that are liquids or solids, the standard state is just the concentration of the substance within the liquid or solid. Because the molar concentrations of pure liquids and solids normally do not vary greatly with temperature, the ratio of the molarity to the standard state for substances that are liquids or solids always has a value of 1. For example, for a compound such as CaF 2 (s), the term going into the equilibrium expression is [CaF 2 ]/[CaF 2 ] which cancels to unity. Thus, when the activities of the solids and liquids (including solvents) are incorporated into the equilibrium expression, they do not change the value.
Consider the following reaction, which is used in the final firing of some types of pottery to produce brilliant metallic glazes:
\[\ce{CO2(g) + C(s) \rightleftharpoons 2CO(g)} \label{Eq14.4.1} \]
The glaze is created when metal oxides are reduced to metals by the product, carbon monoxide. The equilibrium constant expression for this reaction is as follows:
\[K=\dfrac{a_{\ce{CO}}^2}{a_{\ce{CO2}}a_{C}}=\dfrac{[\ce{CO}]^2}{[\ce{CO2}][1]}=\dfrac{[\ce{CO}]^2}{[\ce{CO_2}]}\label{Eq14.4.2} \]
The equilibrium constant for this reaction can also be written in terms of the partial pressures of the gases:
\[K_p=\dfrac{(P_{CO})^2}{P_{CO_2}} \label{Eq14.4.3} \]
Incorporating all the constant values into \(K′\) or \(K_p\) allows us to focus on the substances whose concentrations change during the reaction.
Although the activities of pure liquids or solids are not written explicitly in the equilibrium constant expression, these substances must be present in the reaction mixture for chemical equilibrium to occur. Whatever the concentrations of \(\ce{CO}\) and \(\ce{CO_2}\), the system described in Equation \(\ref{Eq14.4.1}\) will reach chemical equilibrium only if a stoichiometric amount of solid carbon or excess solid carbon has been added so that some is still present once the system has reached equilibrium. As shown in Figure \(\PageIndex{1}\), it does not matter whether 1 g or 100 g of solid carbon is present; in either case, the composition of the gaseous components of the system will be the same at equilibrium.
Example \(\PageIndex{1}\)
Write each expression for \(K\), incorporating all constants, and \(K_p\) for the following equilibrium reactions.
- \(\ce{PCl3(l) + Cl2(g) <=> PCl5(s)}\)
- \(\ce{Fe3O4(s) + 4H2(g) <=> 3Fe(s) + 4H2O(g)}\)
Given : balanced equilibrium equations.
Asked for : expressions for \(K\) and \(K_p\).
Strategy :
Find \(K\) by writing each equilibrium constant expression as the ratio of the concentrations of the products and reactants, each raised to its coefficient in the chemical equation. Then express \(K_p\) as the ratio of the partial pressures of the products and reactants, each also raised to its coefficient in the chemical equation.
Solution
This reaction contains a pure solid (\(PCl_5\)) and a pure liquid (\(PCl_3\)). Their activities are equal to 1, so when incorporated into the equilibrium constant expression, they do not change the value. So
\[K=\dfrac{1}{(1)[Cl_2]} \nonumber \]
and
\[K_p=\dfrac{1}{(1)P_{Cl_2}} \nonumber \]
This reaction contains two pure solids (\(Fe_3O_4\) and \(Fe\)), which are each assigned a value of 1 in the equilibrium constant expressions:
\[K=\dfrac{(1)[H_2O]^4}{(1)[H_2]^4} \nonumber \]
and
\[K_p=\dfrac{(1)(P_{H_2O})^4}{(1)(P_{H_2})^4} \nonumber \]
Exercise \(\PageIndex{1}\)
Write the expressions for \(K\) and \(K_p\) for the following reactions.
- \(\ce{CaCO3(s) <=> CaO(s) + CO2(g)}\)
- \( \underset{glucose}{\ce{C6H12O6(s)}} + \ce{6O2(g) <=> 6CO2(g) + 6H2O(g)}\)
- Answer a
-
\(K = [\ce{CO_2}]\) and \(K_p = P_{\ce{CO_2}}\)
- Answer b
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\(K=\dfrac{[CO_2]^6[H_2O]^6}{[O_2]^6}\) and \(K_p=\dfrac{(P_{CO_2})^6(P_{H_2O})^6}{(P_{O_2})^6}\)
For reactions carried out in solution, the solvent is assumed to be pure, and therefore is assigned an activity equal to 1 in the equilibrium constant expression. The activities of the solutes are approximated by their molarities. The result is that the equilibrium constant expressions appear to only depend upon the concentrations of the solutes.
The activities of pure solids, pure liquids, and solvents are defined as having a value of '1'. Often, it is said that these activities are "left out" of equilibrium constant expressions. This is an unfortunate use of words. The activities are not "left out" of equilibrium constant expressions. Rather, because they have a value of '1', they do not change the value of the equilibrium constant when they are multiplied together with the other terms. The activities of the solutes are approximated by their molarities.
Summary
An equilibrated system that contains products and reactants in a single phase is a homogeneous equilibrium; a system whose reactants, products, or both are in more than one phase is a heterogeneous equilibrium.
Contributors and Attributions
- Anonymous
- Modified by Tom Neils (Grand Rapids Community College)


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3.E: Composition of Substances and Solutions- Homework
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For Chapter 3 you MUST know:
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The additional polyatomic ions: cyanide ( \(\ce{CN^-}\)), nitrite ( \(\ce{NO_2^-}\)), and sulfite ( \(\ce{SO_3^{2-}}\)).
Turn in your answers for the following questions - show your work
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For the following molecules; write the chemical formula, determine the molecular weight and determine the number of moles in exactly 1 gram.
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carbon dioxide
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iron (II) chloride
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dinitrogen pentoxide
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iron (III) sulfate
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Name the following compounds, determine the molecular weight and determine how many moles in 8.35 grams of the compound.
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KI
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CaF
2
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Cu
2
SO
4
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N
2
O
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LiOH
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Give the chemical formula (or atomic symbol), molecular (or atomic) weight, and charge for the following ions:
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sulfate
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sulfite
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nitrate
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chloride
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nitride
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acetate
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carbonate
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Calculate the number of moles in:
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45.3594 g of Ne
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0.198669 g of Ne
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Calculate the mass of:
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2.00 mole of Fe
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4.362 x 10
-5
mol of Fe
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Describe how to prepare 250 mL of 0.12 M lithium chloride solution from solid lithium chloride.
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Describe how to prepare 100 mL of 0.012 M lithium chloride solution from a 0.12 M lithium chloride solution.
The Following Questions are for your practice - Do Not Turn In. They include answers so you can check your work
3.1: Formula Mass and the Mole Concept
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What is the total mass (amu) of carbon in each of the following molecules?
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CH
4
-
C
12
H
10
O
6
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(a) 12.01 amu; (b) 144.12 amu
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Calculate the molecular or formula mass of each of the following:
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P
4
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H
2
O
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Ca(NO
3
)
2
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(a) 123.896 amu; (b) 18.015 amu; (c) 164.086 amu
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Determine the molecular mass of the following compounds:
-
-
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(a) 56.107 amu; (b) 54.091 amu;
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Calculate the molar mass of each of the following:
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S
8
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C
5
H
12
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(a) 256.528 g/mol; (b) 72.150 g mol
−1
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Determine the mass of each of the following:
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0.0146 mol KOH
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10.2 mol ethane, C
2
H
6
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(a) 0.819 g; (b) 307 g;
3.2: Determining Empirical and Molecular Formulas
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Calculate the percent composition of ammonia, NH
3
to four significant figures:
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(a) % N = 82.24%; % H = 17.76%
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A compound of carbon and hydrogen contains 92.3% C and has a molar mass of 78.1 g/mol. What is its molecular formula?
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(a) C
6
H
6
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Determine the empirical and molecular formula for chrysotile asbestos. Chrysotile has the following percent composition: 28.03% Mg, 21.60% Si, 1.16% H, and 49.21% O. The molar mass for chrysotile is 520.8 g/mol.
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(a) Mg
3
Si
2
H
3
O
8
(empirical formula), Mg
6
Si
4
H
6
O
16
(molecular formula)
3.3: Molarity
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Determine the molarity for 0.444 mol of CoCl
2
in 0.654 L of solution
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(a) 0.679
M
;
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Determine the molarity for 98.0 g of phosphoric acid, H
3
PO
4
, in 1.00 L of solution
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(a) 1.00
M
;
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Calculate the number of moles and the mass of the solute in 2.00 L of 18.5
M
H
2
SO
4
, concentrated sulfuric acid:
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(a) 37.0 mol H
2
SO
4
; 3.63 × 10
3
g H
2
SO
4
;
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Calculate the molarity of 0.195 g of cholesterol, C
27
H
46
O, in 0.100 L of serum, the average concentration of cholesterol in human serum
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(a) 5.04 × 10
−3
M
;
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What is the molarity of the diluted solution when 1.00 L of a 0.250-
M
solution of Fe(NO
3
)
3
is diluted to a final volume of 2.00 L?
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(a) 0.125
M
;
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What volume of a 0.20-
M
K
2
SO
4
solution contains 57 g of K
2
SO
4
?
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(a) 1.6 L


7.2.4: Rip Van Winkle- A Feminist Battle Cry
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- Robin DeRosa, Abby Goode et al.
- Plymouth State University/
Great. Now that I’ve gotten your attention with an exciting title, we can begin. There is no trickery here though. It cannot be denied that the almost two-hundred-year-old text from Washington Irving is one of the most pro-women pieces in early American literature. Why make this insane claim, you ask? The answer is quite simple.
To start, there is a lot said about Rip Van Winkle as a character.  This sentence alone is trying to paint a particular picture of the Van Winkle husband. His “simple” nature is celebrated often in the novel as being a pure and innocent characteristic, but is this the true intention? For although he is praised for his simple nature, he is also described as being an incredibly lazy individual. He does not even consider the idea of working on his family’s farm because he figures it’ll never grow for him anyway (60). What kind of an excuse is this supposed to be anyway? Irving is characterizing Rip as a person who does not want to work to help his family or himself, but there are characters that are seen as hard-working and anything but “simple.”
Consider again the end of the quote from earlier: “an obedient hen-pecked husband.” When we are first introduced to the titular “hero,” we are made aware of his poor relationship with his wife. She is called a “shrew” and is allegedly so mean that she makes Rip’s dog unhappy when he enters the home (61). Is it insane to see her as a positive character? Only if you are someone like Rip Van Winkle. If one is lazy or absent-minded then the wife of Rip would seem to be a negative presence, but this is where the story’s obvious satire comes into play. The narrator of the story, who seemingly admires the innocence and laziness of Rip, declares: “Rip Van Winkle, . . . was one of those happy mortals, of foolish well-oiled dispositions . . . but his wife kept continually dinning in his ears about his idleness, his carelessness, and the ruin h was bringing on his family” (61). Dame Van Winkle is the only one in this story who is trying to ensure the family’s survival. Even after the infamous “deep sleep” of Rip later on, he is greeted and accepted by the townspeople even with his lazy demeanor. His wife, however, continues on without him. She is able to fulfill the role that Rip himself always seemed to run away from. Moreover, the accomplishments of Dame Van Winkle alone are not the only female highlights of the story. After Rip awakens from his twenty year sleep, he runs into his now fully grown daughter Judith.
Judith herself is strong figure in the story who serves as Rip’s safety net on his return home. Upon seeing her father again for the first time, who she believed to have run away or been killed, she does not react angrily, but immediately brings him into her home without much explanation (68-69). Like her mother before her ,Judith has managed to make something of her life through hard work, and when her lazy father returns with nothing, she welcomes him back with no harsh words.
The female characters of the story are the true heroes of the story. The narrator and Rip both share a male perspective on the story, reducing women’s criticisms to “nagging,” and rendering them invalid. Rip Van Winkle’s son of the same name also shares his father’s same personality and is equally as ostracized by his family. He is first seen by Rip Sr. leaning against a tree doing absolutely nothing at all (67). There is a clear cycle on display here.  Once again, a female Van Winkle is caring for a family. And yet again Rip Sr. has not learned his lesson and remained as lazy as the day he started his sleep, letting the women of his family do all the work.


1.2: Random Sampling
Now that you know that you have to take samples in order to gather data, the next question is how best to gather a sample? There are many ways to take samples. Not all of them will result in a representative sample. Also, just because a sample is large does not mean it is a good sample. As an example, you can take a sample involving one million people to find out if they feel there should be more gun control, but if you only ask members of the National Rifle Association (NRA) or the Coalition to Stop Gun Violence, then you may get biased results. You need to make sure that you ask a cross-section of individuals. Let’s look at the types of samples that can be taken. Do realize that no sample is perfect, and may not result in a representation of the population.
Census: An attempt to gather measurements or observations from all of the objects in the entire population.
A true census is very difficult to do in many cases. However, for certain populations, like the net worth of the members of the U.S. Senate, it may be relatively easy to perform a census. We should be able to find out the net worth of each and every member of the Senate since there are only 100 members. But, when our government tries to conduct the national census every 10 years, you can believe that it is impossible for them to gather data on each and every American.
The best way to find a sample that is representative of the population is to use a random sample. There are several different types of random sampling. Though it depends on the task at hand, the best method is often simple random sampling which occurs when you randomly choose a subset from the entire population.
Simple Random Sample: Every sample of size n has the same chance of being chosen, and every individual in the population has the same chance of being in the sample.
An example of a simple random sample is to put all of the names of the students in your class into a hat, and then randomly select five names out of the hat.
Stratified Sampling: This is a method of sampling that divides a population into different groups, called strata, and then takes random samples inside each strata.
An example where stratified sampling is appropriate is if a university wants to find out how much time their students spend studying each week; but they also want to know if different majors spend more time studying than others. They could divide the student body into the different majors (strata), and then randomly pick a number of people in each major to ask them how much time they spend studying. The number of people asked in each major (strata) does not have to be the same.
Systematic Sampling: This method is where you pick every kth individual, where k is some whole number. This is used often in quality control on assembly lines.
For example, a car manufacturer needs to make sure that the cars coming off the assembly line are free of defects. They do not want to test every car, so they test every 100th car. This way they can periodically see if there is a problem in the manufacturing process. This makes for an easier method to keep track of testing and is still a random sample.
Cluster Sampling: This method is like stratified sampling, but instead of dividing the individuals into strata, and then randomly picking individuals from each strata, a cluster sample separates the individuals into groups, randomly selects which groups they will use, and then takes a census of every individual in the chosen groups.
Cluster sampling is very useful in geographic studies such as the opinions of people in a state or measuring the diameter at breast height of trees in a national forest. In both situations, a cluster sample reduces the traveling distances that occur in a simple random sample. For example, suppose that the Gallup Poll needs to perform a public opinion poll of all registered voters in Colorado. In order to select a good sample using simple random sampling, the Gallup Poll would have to have all the names of all the registered voters in Colorado, and then randomly select a subset of these names. This may be very difficult to do. So, they will use a cluster sample instead. Start by dividing the state of Colorado up into categories or groups geographically. Randomly select some of these groups. Now ask all registered voters in each of the chosen groups. This makes the job of the pollsters much easier, because they will not have to travel over every inch of the state to get their sample but it is still a random sample.
Quota Sampling: This is when the researchers deliberately try to form a good sample by creating a cross-section of the population under study.
For an example, suppose that the population under study is the political affiliations of all the people in a small town. Now, suppose that the residents of the town are 70% Caucasian, 25% African American, and 5% Native American. Further, the residents of the town are 51% female and 49% male. Also, we know information about the religious affiliations of the townspeople. The residents of the town are 55% Protestant, 25% Catholic, 10% Jewish, and 10% Muslim. Now, if a researcher is going to poll the people of this town about their political affiliation, the researcher should gather a sample that is representative of the entire population. If the researcher uses quota sampling, then the researcher would try to artificially create a cross-section of the town by insisting that his sample should be 70% Caucasian, 25% African American, and 5% Native American. Also, the researcher would want his sample to be 51% female and 49% male. Also, the researcher would want his sample to be 55% Protestant, 25% Catholic, 10% Jewish, and 10% Muslim. This sounds like an admirable attempt to create a good sample, but this method has major problems with selection bias.
The main concern here is when does the researcher stop profiling the people that he will survey? So far, the researcher has cross-sectioned the residents of the town by race, gender, and religion, but are those the only differences between individuals? What about socioeconomic status, age, education, involvement in the community, etc.? These are all influences on the political affiliation of individuals. Thus, the problem with quota sampling is that to do it right, you have to take into account all the differences among the people in the town. If you cross-section the town down to every possible difference among people, you end up with single individuals, so you would have to survey the whole town to get an accurate result. The whole point of creating a sample is so that you do not have to survey the entire population, so what is the point of quota sampling?
Note: The Gallup Poll did use quota sampling in the past, but does not use it anymore.
As the name of this sampling technique implies, the basis of convenience sampling is to use whatever method is easy and convenient for the investigator. This type of sampling technique creates a situation where a random sample is not achieved. Therefore, the sample will be biased since the sample is not representative of the entire population.
For example, if you stand outside the Democratic National Convention in order to survey people exiting the convention about their political views. This may be a convenient way to gather data, but the sample will not be representative of the entire population.
Of all of the sampling types, a random sample is the best type. Sometimes, it may be difficult to collect a perfect random sample since getting a list of all of the individuals to randomly choose from may be hard to do.
Determine if the sample type is simple random sample, stratified sample, systematic sample, cluster sample, quota sample, or convenience sample.
Solution
- A researcher wants to determine the different species of trees that are in the Coconino National Forest. She divides the forest using a grid system. She then randomly picks 20 different sections and records the species of every tree in each of the chosen sections.
This is a cluster sample, since she randomly selected some of the groups, and all individuals in the chosen groups were surveyed.
- A pollster stands in front of an organic foods grocery store and asks people leaving the store how concerned they are about pesticides in their food.
This is a convenience sample, since the person is just standing out in front of one store. Most likely the people leaving an organic food grocery store are concerned about pesticides in their food, so the sample would be biased.
- The Pew Research Center wants to determine the education level of mothers. They randomly ask mothers to say if they had some high school, graduated high school, some college, graduated from college, or advance degree.
This is a simple random sample, since the individuals were picked randomly.
- Penn State wants to determine the salaries of their graduates in the majors of agricultural sciences, business, engineering, and education. They randomly ask 50 graduates of agricultural sciences, 100 graduates of business, 200 graduates of engineering, and 75 graduates of education what their salaries are.
This is a stratified sample, since all groups were used, and then random samples were taken inside each group.
- In order for the Ford Motor Company to ensure quality of their cars, they test every 130th car coming off the assembly line of their Ohio Assembly Plant in Avon Lake, OH.
This is a systematic sample since they picked every 130th car.
- A town council wants to know the opinion of their residents on a new regional plan. The town is 45% Caucasian, 25% African American, 20% Asian, and 10% Native American. It also is 55% Christian, 25% Jewish, 12% Islamic, and 8% Atheist. In addition, 8% of the town did not graduate from high school, 12% have graduated from high school but never went to college, 16% have had some college, 45% have obtained bachelor’s degree, and 19% have obtained a post-graduate degree. So the town council decides that the sample of residents will be taken so that it mirrors these breakdowns.
This is a quota sample, since they tried to pick people who fit into these subcategories.


6.2: The Solid State of Matter
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Learning Objectives
By the end of this section, you will be able to:
- Define and describe the bonding and properties of ionic, molecular, metallic, and covalent network crystalline solids
- Describe the main types of crystalline solids: ionic solids, metallic solids, covalent network solids, and molecular solids
- Explain the ways in which crystal defects can occur in a solid
When most liquids are cooled, they eventually freeze and form crystalline solids , solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern. It is also possible for a liquid to freeze before its molecules become arranged in an orderly pattern. The resulting materials are called amorphous solids or noncrystalline solids (or, sometimes, glasses). The particles of such solids lack an ordered internal structure and are randomly arranged ( Figure 10.37 ).
Metals and ionic compounds typically form ordered, crystalline solids. Substances that consist of large molecules, or a mixture of molecules whose movements are more restricted, often form amorphous solids. For examples, candle waxes are amorphous solids composed of large hydrocarbon molecules. Some substances, such as silicon dioxide (shown in Figure 10.38 ), can form either crystalline or amorphous solids, depending on the conditions under which it is produced. Also, amorphous solids may undergo a transition to the crystalline state under appropriate conditions.
Crystalline solids are generally classified according to the nature of the forces that hold its particles together. These forces are primarily responsible for the physical properties exhibited by the bulk solids. The following sections provide descriptions of the major types of crystalline solids: ionic, metallic, covalent network, and molecular.
Ionic Solids
Ionic solids , such as sodium chloride and nickel oxide, are composed of positive and negative ions that are held together by electrostatic attractions, which can be quite strong ( Figure 10.39 ). Many ionic crystals also have high melting points. This is due to the very strong attractions between the ions—in ionic compounds, the attractions between full charges are (much) larger than those between the partial charges in polar molecular compounds. This will be looked at in more detail in a later discussion of lattice energies. Although they are hard, they also tend to be brittle, and they shatter rather than bend. Ionic solids do not conduct electricity; however, they do conduct when molten or dissolved because their ions are free to move. Many simple compounds formed by the reaction of a metallic element with a nonmetallic element are ionic.
Metallic Solids
Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms Figure 10.40 . The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties. All exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many are very hard and quite strong. Because of their malleability (the ability to deform under pressure or hammering), they do not shatter and, therefore, make useful construction materials. The melting points of the metals vary widely. Mercury is a liquid at room temperature, and the alkali metals melt below 200 °C. Several post-transition metals also have low melting points, whereas the transition metals melt at temperatures above 1000 °C. These differences reflect differences in strengths of metallic bonding among the metals.
Covalent Network Solid
Covalent network solids include crystals of diamond, silicon, some other nonmetals, and some covalent compounds such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds. The atoms in these solids are held together by a network of covalent bonds, as shown in Figure 10.41 . To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically characterized by hardness, strength, and high melting points. For example, diamond is one of the hardest substances known and melts above 3500 °C.
Molecular Solid
Molecular solids , such as ice, sucrose (table sugar), and iodine, as shown in Figure 10.42 , are composed of neutral molecules. The strengths of the attractive forces between the units present in different crystals vary widely, as indicated by the melting points of the crystals. Small symmetrical molecules (nonpolar molecules), such as H 2 , N 2 , O 2 , and F 2 , have weak attractive forces and form molecular solids with very low melting points (below −200 °C). Substances consisting of larger, nonpolar molecules have larger attractive forces and melt at higher temperatures. Molecular solids composed of molecules with permanent dipole moments (polar molecules) melt at still higher temperatures. Examples include ice (melting point, 0 °C) and table sugar (melting point, 185 °C).
Properties of Solids
A crystalline solid, like those listed in Table 10.4 , has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Thus, the attractions between the units that make up the crystal all have the same strength and all require the same amount of energy to be broken. The gradual softening of an amorphous material differs dramatically from the distinct melting of a crystalline solid. This results from the structural nonequivalence of the molecules in the amorphous solid. Some forces are weaker than others, and when an amorphous material is heated, the weakest intermolecular attractions break first. As the temperature is increased further, the stronger attractions are broken. Thus amorphous materials soften over a range of temperatures.
| Type of Solid | Type of Particles | Type of Attractions | Properties | Examples |
|---|---|---|---|---|
| ionic | ions | ionic bonds | hard, brittle, conducts electricity as a liquid but not as a solid, high to very high melting points | NaCl, Al 2 O 3 |
| metallic | atoms of electropositive elements | metallic bonds | shiny, malleable, ductile, conducts heat and electricity well, variable hardness and melting temperature | Cu, Fe, Ti, Pb, U |
| covalent network | atoms of electronegative elements | covalent bonds | very hard, not conductive, very high melting points | C (diamond), SiO 2 , SiC |
| molecular | molecules (or atoms) | IMFs | variable hardness, variable brittleness, not conductive, low melting points | H 2 O, CO 2 , I 2 , C 12 H 22 O 11 |
How Sciences Interconnect
Graphene: Material of the Future
Carbon is an essential element in our world. The unique properties of carbon atoms allow the existence of carbon-based life forms such as ourselves. Carbon forms a huge variety of substances that we use on a daily basis, including those shown in Figure 10.43 . You may be familiar with diamond and graphite, the two most common allotropes of carbon. (Allotropes are different structural forms of the same element.) Diamond is one of the hardest-known substances, whereas graphite is soft enough to be used as pencil lead. These very different properties stem from the different arrangements of the carbon atoms in the different allotropes.
You may be less familiar with a recently discovered form of carbon: graphene. Graphene was first isolated in 2004 by using tape to peel off thinner and thinner layers from graphite. It is essentially a single sheet (one atom thick) of graphite. Graphene, illustrated in Figure 10.44 , is not only strong and lightweight, but it is also an excellent conductor of electricity and heat. These properties may prove very useful in a wide range of applications, such as vastly improved computer chips and circuits, better batteries and solar cells, and stronger and lighter structural materials. The 2010 Nobel Prize in Physics was awarded to Andre Geim and Konstantin Novoselov for their pioneering work with graphene.


17.3B: Microscopic Anatomy
Cardiac muscle appears striated due to the presence of sarcomeres, the highly-organized basic functional unit of muscle tissue.
- Identify the microscopic anatomy of cardiac muscles
Key Points
- Cardiac muscle, composed of the contractile cells of the heart, has a striated appearance due to alternating thick and thin filaments composed of myosin and actin.
- Actin and myosin are contractile protein filaments, with actin making up thin filaments, and myosin contributing to thick filaments. Together, they are considered myofibrils.
- Myosin and actin adenosine triphosphate ( ATP ) binding allows for muscle contraction. It is regulated by action potentials and calcium concentrations.
- Adherens junctions, gap junctions, and desmosomes are intercalated discs that connect cardiac muscle cells. Gap junctions specifically allow for the transmission of action potentials within cells.
Key Terms
- intercalated discs : Junctions that connect cardiomyocytes together, some of which transmit electrical impulses between cells.
- sarcomere : The basic unit of contractile muscle which contains myosin and actin, the two proteins that slide past one another to cause a muscle contraction.
Cardiac muscle, like skeletal muscle, appears striated due to the organization of muscle tissue into sarcomeres. While similar to skeletal muscle, cardiac muscle is different in a few ways. Cardiac muscles are composed of tubular cardiomyocytes, or cardiac muscle cells. The cardiomyocytes are composed of tubular myofibrils, which are repeating sections of sarcomeres. Intercalated disks transmit electrical action potentials between sarcomeres.
Sarcomere Structure
A sarcomere is the basic unit of muscle tissue in both cardiac and skeletal muscle. Sarcomeres appear under the microscope as striations, with alternating dark and light bands. Sarcomeres are connected to a plasma membrane, called a sarcolemma, by T-tubules, which speed up the rate of depolarization within the sarcomere.
Individual sarcomeres are composed of long, fibrous proteins that slide past each other when the muscles contract and relax. The two most important proteins within sarcomeres are myosin, which forms a thick, flexible filament, and actin, which forms the thin, more rigid filament. Myosin has a long, fibrous tail and a globular head which binds to actin. The myosin head also binds to ATP, the source of energy for muscle movement. Actin molecules are bound to the Z-disc, which forms the borders of the sarcomere. Together, myosin and actin form myofibrils, the repeating molecular structure of sarcomeres.
Myofibril activity is required for muscle contraction on the molecular level. When ATP binds to myosin, it separates from the actin of the myofibril, which causes a contraction. Muscle contraction is a complex process regulated by calcium influx and the stimulus of electrical impulses.
Muscle Contraction and Actin-Myosin Interactions : Skeletal muscle contracts following activation by an action potential. Binding of Acetylcholine at the motor end plate leads to intracellular calcium release and interactions between myofibrils, eliciting contraction.
The Sarcomere : A single sarcomere unit with all functional areas labeled, including thick and thin filaments, Z lines, H zone, I bands, and A band.
Intercalated Discs
Intercalated discs are gap junctions that link cardiomyocytes so that electrical impulses (action potentials) can travel between cells. In a more general sense, an intercalated disk is any junction that links cells together between a gap in which no other cells exist, such as an extracellular matrix. In cardiac muscle tissue, they are also responsible for transmission of action potentials and calcium during muscle contraction. In cardiac muscle, intercalated discs connecting cardiomyocytes to the syncytium, a multinucleated muscle cell, to support the rapid spread of action potentials and the synchronized contraction of the myocardium. Intercalated discs consist of three types of cell-cell junctions, most of which are found in other tissues besides cardiac muscle:
- Adherens junctions, which anchor actin filaments to cytoplasm of cardiomyocytes.
- Desmosomes, which bind adhesion proteins to the cytoskeleton within cells, thus connecting the cells.
- Gap junctions, which connect proteins to the cytoplasm of different cells and transmit action potentials between both cells, required for cellular depolarization. It is found primarily in nervous and muscular tissue.
Under light microscopy, intercalated discs appear as thin lines dividing adjacent cardiac muscle cells and running perpendicular to the direction of muscle fibers.


11.5: Spotlight Application
Elyn Saks, a professor of law, psychology, and psychiatry at USC, shares her experience of living with schizophrenia in a 15-minute TEDGlobal video [1] : “ Elyn Saks: A Tale of Mental Illness– From the Inside .”
Reflective Questions:
- What strikes you most about Dr. Sak’s journey with schizophrenia?
- What are three takeaways points from Dr. Sak’s presentation?
View the following YouTube video on “ What Living Well With Schizophrenia Means to Me ” [2]
Reflective Questions:
- How is X’s journey with schizophrenia different from Dr. Sak’s?
- What are three things you learned from X’s description of her journey with schizophrenia?
- TEDGlobal. (2012). A Tale of Mental Illness -- From the Inside. [Video]. TED. All rights reserved. https://www.ted.com/talks/elyn_saks_seeing_mental_illness ↵
- Living Well with Schizophrenia. (2020, March 7). What living well with schizophrenia means to me [Video]. YouTube. All rights reserved. https://youtu.be/VUhw64iEIQw ↵


12: Respiratory System Infections (Part A)
The respiratory tract is one of the main portals of entry into the human body for microbial pathogens. On average, a human takes about 20,000 breaths each day. This roughly corresponds to 10,000 liters, or 10 cubic meters, of air. Suspended within this volume of air are millions of microbes of terrestrial, animal, and human origin—including many potential pathogens. A few of these pathogens will cause relatively mild infections like sore throats and colds. Others, however, are less benign. According to the World Health Organization, respiratory tract infections such as tuberculosis, influenza, and pneumonia were responsible for more than 4 million deaths worldwide in 2012. [1]
Chapter Outline
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- 12.1: Viral Infections of the Respiratory Tract
- Viruses cause respiratory tract infections more frequently than bacteria, and most viral infections lead to mild symptoms. The common cold can be caused by more than 200 viruses, typically rhinoviruses, coronaviruses, and adenoviruses, transmitted by direct contact, aerosols, or environmental surfaces. Due to its ability to rapidly mutate through antigenic drift and antigenic shift, influenza remains an important threat to human health. Two new influenza vaccines are developed annually.
Footnotes
- World Health Organization. “The Top Ten Causes of Death.” May 2014. http://www.who.int/mediacentre/factsheets/fs310/en/


3.4: Patterns of Biodiversity
Developing a strategy to conserve biodiversity requires a firm understanding of where threatened species and populations occur, why they are threatened, what their needs are, and what role they play in their respective ecosystems. By obtaining an understanding of species’ distributions, biologists simultaneously gain an initial rough “estimate” of genetic diversity and ecosystem diversity. While addressing these questions is a critical task, finding appropriate answers can be complex, expensive, and take a long time to solve. This is in no small part because identifying species can, at times, be a very challenging endeavour.
Challenging species identifications
Before biologists can determine a species’ distribution, needs, and population status, it is important to know the identity of the individuals being studied. While this may sound like a straightforward task, the process of identifying (and naming) a species can be deceptively hard, even for professional taxonomist. For example, a recent study found that 58% of 4,500 wild African ginger (Aframomum spp.) specimens that were deposited by professional biologists across 40 herbaria in 21 countries were given the wrong name (Goodwin et al., 2015)!
Describing species can be difficult, in part, because the multiple methods used by biologists to separate species do not always give the same results.
Identifying species can be hard, in part because the three tests biologists use to separate different species—morphology, biology, and evolution—do not always give the same results. That is because the methods and assumptions of each test are different. For example, some species have several varieties with easily observed morphological differences but are biologically and genetically similar enough that all those varieties are still considered a single species. A well-known example is the single species Canis familiaris, or domestic dog, whose wildly variable and numerous breeds can interbreed despite their large morphological differences. In contrast, some butterflies are considered distinct species because they cannot interbreed and have a characteristic genetic makeup, even though they cannot be separated by the naked eye.
Another important aspect complicating species identifications is that speciation—whereby one species evolves into another—is a slow and gradual process; for some species, it may take many thousands of years. Consequently, much controversy exists about where to draw the “new species” line; in other words, when is a species distinct enough to be considered a separate species? Africa’s iconic giraffes (Giraffa camelopardalis, VU) are a case in point. Taxonomists recently suggested that the region’s giraffes—previously considered a single species—may, in fact, consist of four (Fennessy et al., 2016) or even six (Brown et al., 2007) species. Unfortunately, the final number of giraffe species is still disputed because of the different assumptions made by each study and how that impacts the number of species (Bercovitch et al., 2017). Similarly, biologists often struggle to split and identify cryptic species—undescribed species that are wrongly grouped with other similar-appearing species. A recent study estimated that 60% of newly discovered species are cryptic (Ceballos and Ehrlich, 2009). Even well-known groups may suffer from this problem: there is a reasonable chance that the bushbuck (Tragelaphus scriptus. LC) and klipspringer (Oreotragus oreotragus, LC) may in fact consist of several cryptic species yet to be described (Plumptre and Wronski, 2013; Groves et al., 2017).
Hybridisation plays an important role in speciation, but it can also be detrimental to conservation efforts, particularly when it involves rare species and/or human disturbance.
To complicate matters even further, some species are closely related enough that they sometimes mate and produce hybrids. These hybrids blur the distinction between species, particularly those that may be early in the process of speciation. For some taxa, hybridisation naturally occurs in areas where the distribution ranges of related species overlap (e.g. de Jong and Butynski, 2010). Such natural hybridisation plays an important role in speciation (the evolution of new species); for example, it may have contributed to the high diversity of cichlid fishes in Africa’s Rift Valley lakes (Salzburger et al., 2002). But hybridisation can also be detrimental to conservation efforts, particularly when it involves rare species and/or human disturbance. For example, when humans reduce one species’ populations so much that they struggle to find reproductive partners of their own kind (e.g. vaz Pinto et al., 2016), when humans remove dispersal barriers that kept related species apart (e.g. Mondol et al., 2015), or when humans force related species that naturally occupy separate distributions to live together through translocations (e.g. Grobler et al., 2011; Benjamin-Fink and Reilly, 2017; van Wyk et al., 2017). While some hybrids may be sterile and thus unable to reproduce, at other times the resulting offspring can be quite strong in an evolutionary sense—a condition known as hybrid vigour (or heterosis)—and may outcompete their parent species. Such is the case with a land snail from the Seychelles (Pachnodus velutinus, EX), which was recently driven to extinction by hybridisation with a closely-related species (Gerlach, 2009)—hybrid individuals can still be found where P. valutinus used to occur.
Conversely, there may also be times when conservation biologists get it wrong and prioritise a species that does not warrant specific status. The Liberian greenbul (Phyllastrephus leucolepis) is one such example. Known from only a handful of records, this species was considered Critically Endangered until 2016, when geneticists discovered that the Liberian greenbul was the same species as the common icterine greenbul (Phyllastrephus icterinus, LC), but with an unusual coloration due to nutrient deficiencies (Collinson et al., 2018).
Implications of challenging species identifications
The difficulties in distinguishing between species have several practical conservation implications. First, when it is hard to identify a species, it may also be hard to determine that species’ true population size and distribution which, in turn, impacts its conservation status. This was illustrated in a study on bushmeat markets in Guinea-Bissau, which showed how primate misidentifications hide the true impact of hunting on some of the region’s most impacted species (Minhós et al., 2013). It also hampers captive breeding projects, by making the captive populations susceptible to outbreeding depression , which occurs when individuals that are not closely related (i.e. from different populations) breed and produce offspring (Conservation genetics is discussed in more detail in Section 8.7). Lastly, identification challenges with cryptic species can also cause delays in the formal description process, a necessary step in writing effective laws to protect them. The recent controversy among biologists arguing whether Africa’s elephants are one or two species is a case in point. African elephants were already considered threatened when biologists thought they were a single species. This all changed in 2005, when taxonomic authorities officially recognized two elephant species, in effect dividing a single threatened species into two (thus even more imperilled) species (CBD, 2015). Yet, to avoid leaving hybrid elephants (e.g. Mondol et al., 2015) with an uncertain conservation status, the IUCN continues to assess elephants as one single species (Blanc, 2008); thus, their current Vulnerable assessment may not be an accurate reflection of each species’ true conservation status.
Despite these challenges, conservationist biologists need to make every effort to obtain correct identifications. For most studies, morphological methods may be adequate. But when there is doubt, it is important for researchers to confirm their identifications with additional methods. Recent progress in making genetic technology more widely accessible through hand-held devices (Pennisi, 2016; Parker et al., 2017) and techniques such as DNA barcoding has also greatly enhanced our ability to correctly classify cryptic species, allowing us to give those species the conservation attention they deserve (Box 3.2).
Sarita Maree 1,2 and Samantha Mynhardt 2
1 Department of Genetics, &
2 Department of Zoology and Entomology,
University of Pretoria, South Africa.
<EMAIL_ADDRESS><EMAIL_ADDRESS>Golden moles (Chrysochloridae) are small, subterranean insectivores that rank among Africa’s most unique, most threatened, and yet poorly studied mammals thanks to their secretive burrowing lifestyle. Ten of the 21 known species are currently threatened with extinction (IUCN, 2019) as their highly restricted and naturally fragmented sandy soil habitats are under threat from human activities. Current conservation efforts are severely jeopardised by taxonomic uncertainties and ambiguous evolutionary relationships, thus far based on morphological and limited genetic data, which suggest that many distinct but cryptic species remain undescribed (Taylor et al., 2018).
To remedy the dearth in knowledge on two endemic South African golden mole species, we analysed molecular data of individuals collected across the entire distribution range of both Juliana’s golden mole (Neamblysomus julianae, EN) and Hottentot golden mole (Amblysomus hottentotus, LC) (Figure 3.B). In contrast to the widespread Hottentot golden mole, the Juliana’s golden mole counts among South Africa’s most imperilled mammals and is known from only three range-restricted, geographically isolated populations (Maree, 2015, Maree et al., 2016; Maree, 2017; Taylor et al., 2018). These three populations, together covering less than 160 km 2 occur in southeastern Pretoria (Gauteng population), the district of Modimolle (Limpopo, ~ 120 km north of Pretoria), and in southwestern Kruger National Park (Mpumalanga, ~ 400 km east of Pretoria) (Figure 3.C).
Using molecular and other genetic methods, we have gained insights about the evolutionary relationships and gene flow between these two golden mole species, which have several conservation implications. First, preliminary findings suggest that the Hottentot golden mole contains several morphologically similar, but evolutionary distinct and genetically divergent lineages, some of which would represent undescribed cryptic species (Mynhardt et al., 2015; Taylor et al., 2018). Similarly, preliminary evidence suggests the Juliana’s golden mole contains pronounced genetic separation between the Mpumalanga population and the Gauteng and Limpopo populations. This also corresponds to morphological differences observed between these populations, which collectively suggest that the Mpumalanga population of Juliana’s golden mole might in fact be a cryptic species (Maree, 2015; Maree et al., 2016; Maree, 2017; Taylor et al., 2018). Unfortunately, in each of these cases the knowledge gaps remaining precluded definitive conclusions. Rigorous geographic sampling and additional molecular/genomic analyses will be needed to confirm the taxonomic status and geographic boundaries of putative new species within these and other golden mole taxa (Taylor et al., 2018).
Our results show that genetic frameworks contribute substantially to informed conservation decision-making. For golden moles and other taxa, some newly described species will undoubtedly be considered more threatened than in their previous species designations. Threat assessments on the Juliana’s golden mole has already identified the Gauteng population as Critically Endangered due to severe habitat loss and transformation within its highly restricted and already fragmented range (~ 22 km 2 in extent) caused by rapid urbanisation and opencast sand mining. This pressure is exacerbated by this species’ extreme habitat specificity and poor dispersal capabilities (Jackson and Robertson, 2011; Maree, 2015; Maree et al., 2016; Maree, 2017; Taylor et al., 2018). Species distribution modelling (SDM, discussed in Section 10.1.1) predicted several regions throughout Gauteng, Mpumalanga, and Limpopo Provinces where the species could potentially occur, but subsequent surveys led to the discovery of only two new localities around Modimolle (Jackson and Robertson, 2011). This finding emphasises that the protection of all suitable habitats remaining for the species and the Pretoria population, in particular, would be key to its persistence. Strategies to achieve this ought to be incorporated into current conservation planning (Maree, 2015; Maree et al., 2016; Maree, 2017; Taylor et al., 2018).
We also illustrated the importance of maintaining the integrity of geographically isolated and/or genetically unique populations, lest yet undescribed species be lost to extinction before they could be fully recognized. A sound taxonomy, obtained through genetic analyses, thus contributes substantially to informed conservation decision-making. Even in the absence of such information, it is still crucial that isolated populations be managed as distinct units to conserve the evolutionary history of different species and populations.
Because the demand for expert taxonomists outstrips their availability, there is also a need to train and employ more taxonomists, particularly in the tropics and other species-rich areas. The public can help in this endeavour. In 2015, citizen scientists—volunteers participating in scientific projects—discovered 51 of 60 new dragonfly species from Africa that were described that year (Dijkstra et al., 2015). For conservation biologists, it is also important to not become despondent about the lagging efforts to describe species. They should instead take an example from motivated parrot lovers who were motivated to work even harder to get their study species recognized as distinct (Box 3.3). It is also important to keep in mind that species are never fixed; evolve all the time, albeit at different rates, due to challenges and opportunities presented by their environment.
Colleen T. Downs
School of Life Sciences, University of KwaZulu-Natal,
Pietermaritzburg, South Africa.
The usefulness of subspecies in conservation has long been a subject of controversy (Coetzer et al., 2015). Accurately drawing the line between an individual species and other similar animals is important for effective studies of biodiversity, and for planning and implementing official conservation strategies. Across Africa, there are many species with very broad historical distributions that are thought to contain locally adapted varieties. However, the distributions of many of these species are now fragmented and disjointed, mainly because of changes in available habitat. Examples include reptiles, such as the Nile crocodile (Crocodylus niloticus, LC), mammals, such as the common hippopotamus (Hippopotamus amphibious, VU), and a wide range of bird species. As a result of this fragmentation, various subspecies, recognized by morphology and habitat distribution, are now recognized as individual species. Modern DNA technology allows these discoveries to be supported with genetic evidence.
Protecting a newly recognized species can be difficult; genetic testing takes time and funding, and if an animal or plant is threatened before it has full species status, conservation success is that much more difficult. An example is the Cape parrot (Poicephalus robustus, EN), a forest species which was first suggested in 1997 to be a separate species and distinct from the more widespread grey-headed parrot (Poicephalus fuscicollis, LC) of Africa’s savannah ecosystems. Additional support for the Cape parrot (Figure 3.D) being a separate species came from ecological and morphological data in 2002 (Wirminghaus et al., 2002) and separate genetic evidence in 2015 (Coetzer et al., 2015). Although many published bird guides reflect the change, the species was recently recognized as a species by authorities (e.g. BirdLife International, 2017), which affected its ability to receive legal protection. The Cape parrot is endemic to South Africa, with a distribution primarily restricted to southern mist-belt Afromontane forests in the Eastern Cape and southern KwaZulu-Natal plus a relict population in Limpopo Province. Cape parrots are restricted in their distribution by their specialised habitat and dietary requirements for particular fruits. A decrease in this species’ abundance over the past 50 years is a consequence of several factors, including habitat fragmentation and degradation, food and nest site shortages, illegal trade of the birds for pets and aviculture, and disease.
Dedicated researchers have recognized the importance of determining population size and raising the awareness of the plight of the Cape parrot and the forests for which it is a flagship species. Current abundance of the Cape parrot is relatively low but stable, with an estimate of fewer than 1,600 birds in the wild (Downs et al., 2014). Estimates are based on an annual census held since 1998, organized by citizen scientists. For the Cape parrot, tardy genetic recognition of full species status was overcome by conservationists’ perseverance. We must be vigilant if we want to protect other still-hidden species from future extinction.
Measuring species diversity
Biologists have developed three quantitative measures of species diversity as a means of measuring and comparing species diversity (Figure 3.7):
- Alpha diversity (or species richness), the most commonly referenced measure of species diversity, refers to the total number of species found in a particular biological community, such as a lake or a forest. Bwindi Forest in Uganda, with an estimated 350 bird species, has one of the highest alpha diversities of all African ecosystems.
- Gamma diversity describes the total number of species that occur across an entire region, such as a mountain range or continent, that includes many ecosystems. The Albertine Rift, which includes Bwindi Forest, has more than 1,074 species of birds, a very high gamma diversity for such a small region.
- Beta diversity connects alpha and gamma diversity. It describes the rate at which species composition changes across a region. For example, if every wetland in a region was inhabited by a similar suite of plant species, then the region would have low beta diversity; in contrast, if several wetlands in a region had plants communities that were distinct and had little overlap with one another, the region would have high beta diversity. Beta diversity is calculated as gamma diversity divided by alpha diversity. The beta diversity for forest birds of the Albertine Rift is about 3.0, if each ecosystem in the area has about the same number of species as Bwindi Forest.
It is important to note that alpha, beta, and gamma diversity describe only part of what is meant by biodiversity. For example, none of these three terms completely account for genetic diversity, which allows species to adapt as conditions change (Section 8.7.1). It also neglects the importance of ecosystem diversity, which results from the collective response of species to their dynamic environment. However, these diversity measures are useful for comparing different regions, and identifying locations with high concentrations of native species that should be protected.
How many species exist?
To date, taxonomists have described about 1.5 million species that share this planet with us (Costello et al., 2012). While this total may seem impressive, available evidence suggests that this estimate vastly underestimates the true extent of Earth’s biodiversity. In fact, even now, after all the exploration in years gone by, several thousand new species are being described each year. Many new discoveries are made by skilled researchers recognizing new species by being able to discern variation in morphological characters; that includes the discoveries of a new small forest antelope from West Africa (Colyn et al., 2010) and a new species of shark off Mozambique (Ebert and Cailliet, 2011). Such discoveries can also be rather surprising and unexpected. For example, an amateur botanist recently discovered two new flowering plants in the heavily studied Cape Floristic Region (Bello et al., 2015). Similarly, the lesula (Cercopithecus lomamiensis)—a species of monkey long known to local hunters—was only formally described after biologists discovered this “different” monkey on a leash in a remote village of the DRC (Hart et al., 2012). Some recent discoveries even include entire new communities in unexpected places. For example, in 2007, grassland surveys by citizen scientists in an area starting 5 km from South Africa’s Johannesburg metropolitan area found previously unknown populations of five threatened bird species, as well as a number of regionally threatened birds and mammals; these discoveries were instrumental in recognizing this area as the Devon Grasslands Important Birding Area (Marnewick et al., 2015).
New genetic technologies have highlighted that there are many thousands of species yet to be described.
The most exciting and newsworthy discoveries of new species generally involve higher-level taxa, especially living fossils. For example, in 1938, biologists across the world were stunned by the report of a strange fish caught in the Indian Ocean off South Africa. This fish, subsequently named coelacanth (Latimeria chalumnae, CR), belongs to a group of marine fishes that were common in ancient seas but were thought to have gone extinct 65 million years ago. Coelacanths are of interest to evolutionary biologists because they show certain features of muscles and bones in their fins that are comparable to the limbs of the first vertebrates that crawled onto land. Following the initial discovery, coelacanths have been found along Africa’s Indian Ocean coast from South Africa to the Comoros and through to Kenya. Unfortunately, the entire coelacanth population, estimated at fewer than 500 individuals, is currently highly threatened because of ongoing fishing pressures (Musick, 2000).
Although field surveys have proven to be of great importance for discovering new species and populations, perhaps the greatest taxonomic progress has come from advances in genetic analyses which help to separate cryptic species previously lumped under more widespread species. For example, advances in genetic research recently highlighted that the African clawed frog (Xenopus laevis, LC)—a popular model organism in biomedical research—consists of seven distinct species (Evans et al., 2015). Similarly, using new genetic methods, scientists recently confirmed that the slender-snouted crocodile (Mecistops cataphractus, CR) consists of two different species, one endemic to West Africa and the other to Central Africa (Shirley et al., 2018).
Estimates suggest there are somewhere between 1–6 billion distinct species on Earth. The most diverse group of species is bacteria.
The presence of so many undiscovered species and communities makes precise estimates of species diversity incredibly difficult, especially in Africa where so many areas remain scientifically unexplored. Our most recent estimates, combining genetic analysis of well-known groups with mathematical patterns, suggests there are between 1–6 billion distinct species on Earth (Table 3.1) of which there are only about 163 million animals and 340 thousand plants (Larsen et al., 2017)—this is obviously much greater than the current catalogue of 1.5 million species! Given the amount of new species that continue to hide in plain sight, so to speak, there is no doubt that a great number of species and communities are waiting to be discovered by eager African adventurers over the next several decades.
|
Kingdom |
Weight (Gt) a |
Number of species (in million) |
% of all species b |
Number of described species c |
% of described species |
|---|---|---|---|---|---|
|
Animals |
2 |
163 |
7 |
1,205,336 |
< 1 |
|
Fungi |
12 |
165 |
7 |
135,110 |
< 0.1 |
|
Plants |
450 |
0.382 c |
< 0.5 |
364,009 |
95 |
|
Chromista |
Unknown |
0.025 c |
< 0.5 |
23,428 |
94 |
|
Protozoans |
4 |
163 |
7 |
2,686 |
0.1 |
|
Archaea |
7 |
0.0005 |
< 0.5 |
377 |
75 |
|
Bacteria |
70 |
1,746 |
78 |
9,982 |
0.1 |
a As gigatonnes of carbon, from Bar-On et al., 2018
b From Larsen et al. (2017)’s Table 1, Scenario 1
Where are most species found?
Because it is so hard to obtain accurate estimates of species numbers, many conservation biologists have recently started to focus their efforts on understanding and planning around patterns of species diversity. This makes sense: regions with many species of one taxon tend to also have many species of other taxa, so protecting one diverse group of species will likely also protect many other species, even if those other species are not well understood. Consequently, many conservation biologists see the forests of the Congo Basin, Albertine Rift, and West Africa as critical conservation priorities because these areas hold Africa’s greatest species concentrations, particularly birds, mammals, and butterflies. But there are very important outliers. For example, due to factors that include the geology and soil characteristics, size and variability of the environment, historical circumstances, or climatic conditions, none of these tropical forest areas have as many plant species as the Cape Floristic Region of South Africa—an area of unparalleled importance for plant diversity. Species diversity relationships may also break down at the local scale; for example, amphibians are likely more diverse in wet, shady riverbeds, whereas reptiles may be more diverse in drier, open habitats even if only tens of metres of space separate the reptiles from a riverbed full of amphibians.
By examining all these patterns of species diversity across the world, biologists have discovered at least two general frameworks governing species richness. The first framework is that stable ecosystems usually have many species, while ecosystems that were subjected to more recent glaciation usually have fewer species. This observation explains why tropical ecosystems are generally considered the world’s most species-rich environments (Table 3.2). While tropical grasslands, wetlands, and other ecosystems all hold relatively high species diversity, species richness of tropical forests are particularly noteworthy; even though these areas occupy only about 7% of Earth’s land surface, they contain over half of the world’s species (Corlett and Primack, 2010). This is, in a large part, due to the relatively large global distribution of the tropical forests and the diversity of geological history between these areas of South and Central America, Africa, Asia, and Australia, which has resulted in unique assemblages of species that have evolved in isolation from each other.
|
Country |
Dominant ecoregion |
Area (× 1000 km 2 ) |
Number of endemic mammals |
Number of native mammals |
Mammals per 1000 km 2 |
|---|---|---|---|---|---|
|
Seychelles |
Oceanic island |
0.45 |
2 |
24 |
53.3 |
|
Cabo Verde |
Oceanic island |
4.03 |
0 |
29 |
7.2 |
|
Rwanda |
Montane forest |
26.8 |
1 |
189 |
7.05 |
|
Eq. Guinea |
Lowland forest |
28.1 |
3 |
184 |
6.55 |
|
Burundi |
Montane forest |
27.8 |
1 |
144 |
5.18 |
|
Sierra Leone |
Varied Forest |
71.7 |
0 |
197 |
2.75 |
|
Zimbabwe |
Savannah |
391 |
0 |
204 |
0.52 |
|
Zambia |
Savannah |
753 |
5 |
242 |
0.32 |
|
Namibia |
Desert |
825 |
3 |
206 |
0.25 |
|
South Africa |
Varied |
1,221 |
31 |
307 |
0.25 |
|
South Sudan |
Sahel |
644 |
1 |
151 |
0.24 |
|
DRC |
Varied |
2,345 |
26 |
438 |
0.19 |
|
Niger |
Sahel |
1,267 |
0 |
134 |
0.11 |
Source: IUCN, 2019.
Tropical forests are not the only species-rich tropical ecosystem. Tropical coral reefs, colonies of tiny aquatic invertebrates that form entire ecosystems (Figure 3.8), are the marine equivalent of tropical forests both in terms of species richness and complexity. These areas not only provide homes for corals, but also for huge numbers of fish, molluscs, and marine mammals that find shelter in these highly productive and sheltered ecosystems. In Africa, tropical coral reefs are most widespread and diverse in coastal East Africa, but unique tropical coral reef communities can also be found along Mozambique and South Africa’s north-eastern coast.
High levels of species diversity, especially among plants, can also be found in ecosystems with a Mediterranean climate, such as southwestern Africa, as well as southwestern Australia, California, central Chile, and the Mediterranean Basin of southern Europe and North Africa. The climate of a Mediterranean-type ecosystem is characterized by cool, moist winters, hot, dry summers, resulting in distinctive plant adaptations such as short twigs and stiff leaves. A combination of special environmental factors, including a considerably old geological age, complex site characteristics (such as varied topography and soils), and frequent fires facilitated rapid speciation and helped to prevent any one species from dominating. Today, although regions with a Mediterranean climate cover only 2% of Earth’s surface, 20% of all plant species are found here (Underwood et al., 2009). The Cape Floristic Region—the only Mediterranean climate in Sub-Saharan Africa—is particularly important to conservationists as it has the highest concentration of higher plant diversity (over 9,000 species) in the world.
The second framework governing pattern of species diversity is that locations with high numbers of species usually hold many endemic species. The Cape Floristic Region, for example, boasts more than 6,200 endemic plant species, which include 12 endemic families and 160 endemic genera. Similarly, Lake Malawi holds nearly 14% of the world’s freshwater fishes (500–1,000 species, totals vary by source), with more than 90% of those being endemic.
Biogeographic transition zones—also known as ecotones—regions where different ecosystems meet and overlap, are a special case of areas that contain great species diversity and high levels of endemicity. These areas share environmental factors of two or more environments, allowing for the mixture of biodiversity from those component environments, while unique features within these areas often also give rise to unique species. A case in point is the Maputaland Centre of Endemism, situated in far southern Mozambique. Here, biological communities from northern tropical and southern temperate ecosystems overlap, resulting in surprisingly high levels of species richness as well as endemism (van Wyk, 1996).
Today is an exciting time of biological exploration. Methods and technologies for exploration are improving rapidly, and we are learning more about the value and function the diversity of life on Earth. As genetic techniques advance and become more accessible, an increasing number of people are participating in recording the presence of species in locations around the world; this includes amateur naturalists and citizen scientists who contribute to bird surveys, plant walks, and other natural history activities. With this increased knowledge of biodiversity also comes an acute awareness that human activities damage ecosystems and reduce diversity. Hopefully this broader awareness will spur more people to take responsibility to protect and restore that biodiversity.


4.3: Jefferson’s Method
Thomas Jefferson proposed a different method for apportionment. After Washington vetoed Hamilton’s method, Jefferson’s method was adopted, and used in Congress from 1791 through 1842. Jefferson, of course, had political reasons for wanting his method to be used rather than Hamilton’s. Primarily, his method favors larger states, and his own home state of Virginia was the largest in the country at the time. He would also argue that it’s the ratio of people to representatives that is the critical thing, and apportionment methods should be based on that. But the paradoxes we saw also provide mathematical reasons for concluding that Hamilton’s method isn’t so good, and while Jefferson’s method might or might not be the best one to replace it, at least we should look for other possibilities.
The first steps of Jefferson’s method are the same as Hamilton’s method. He finds the same divisor and the same quota, and cuts off the decimal parts in the same way, giving a total number of representatives that is less than the required total. The difference is in how Jefferson resolves that difference. He says that since we ended up with an answer that is too small, our divisor must have been too big. He changes the divisor by making it smaller, finding new quotas with the new divisor, cutting off the decimal parts, and looking at the new total, until we find a divisor that produces the required total.
- Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the standard divisor .
- Divide each state’s population by the divisor to determine how many representatives it should have. Record this answer to several decimal places. This answer is called the quota .
- Cut off all the decimal parts of all the quotas (but don’t forget what the decimals were). These are the lower quotas . Add up the remaining whole numbers. This answer will always be less than or equal to the total number of representatives.
- If the total from Step 3 was less than the total number of representatives, reduce the divisor and recalculate the quota and allocation. Continue doing this until the total in Step 3 is equal to the total number of representatives. The divisor we end up using is called the modified divisor or adjusted divisor .
We’ll return to Delaware and apply Jefferson’s method. We begin, as we did with Hamilton’s method, by finding the quotas with the original divisor, \(21,900.82927\):
\(\begin{array}{lrrc}
\text { County } & \text { Population } & \text{ Quota } & \text{ Initial } \\
\hline
\text { Kent } & 162,310 & 7.4111 & 7 \\
\text { Newport } & 538,479 & 24.5872 & 24 \\
\text { Providence } & 197,145 & 9.0017 & 9 \\
\textbf{ Total } & \bf{ 897,934 } & & \bf{ 40 }\end{array}\)
Solution
We need 41 representatives, and this divisor gives only 40. We must reduce the divisor until we get 41 representatives. Let’s try \(21,500\) as the divisor:
\(\begin{array}{lrrc}
\text { County } & \text { Population } & \text{ Quota } & \text{ Initial } \\
\hline
\text { Kent } & 162,310 & 7.5493 & 7 \\
\text { Newport } & 538,479 & 25.0455 & 25 \\
\text { Providence } & 197,145 & 9.1695 & 9 \\
\textbf{ Total } & \bf{ 897,934 } & & \bf{ 41 }\end{array}\)
This gives us the required 41 representatives, so we’re done. If we had fewer than 41, we’d need to reduce the divisor more. If we had more than 41, we’d need to choose a divisor less than the original but greater than the second choice.
Notice that with the new, lower divisor, the quota for New Castle County (the largest county in the state) increased by much more than those of Kent County or Sussex County.
We’ll apply Jefferson’s method for Rhode Island. The original divisor of 14,034.22667 gave these results:
\(\begin{array}{lrrc}
\text { County } & \text { Population } & \text{ Quota } & \text{ Initial } \\
\hline \text { Bristol } & 49,875 & 3.5538 & 3 \\
\text { Kent } & 166,158 & 11.8395 & 11 \\
\text { Newport } & 82,888 & 5.9061 & 5 \\
\text { Providence } & 626,667 & 44.6528 & 44 \\
\text { Washington } & 126,979 & 9.0478 & 9\\
\textbf{ Total } & \bf{ 1,052,567 } & & \bf{ 72 }\end{array}\)
Solution
We need 75 representatives and we only have 72, so we need to use a smaller divisor. Let’s try \(13,500\):
\(\begin{array}{lrrc}
\text { County } & \text { Population } & \text{ Quota } & \text{ Initial } \\
\hline \text { Bristol } & 49,875 & 3.6944 & 3 \\
\text { Kent } & 166,158 & 12.3080 & 12 \\
\text { Newport } & 82,888 & 6.1399 & 6 \\
\text { Providence } & 626,667 & 46.4198 & 46 \\
\text { Washington } & 126,979 & 9.4059 & 9\\
\textbf{ Total } & \bf{ 1,052,567 } & & \bf{ 76 }\end{array}\)
We’ve gone too far. We need a divisor that’s greater than 13,500 but less than \(14,034.22667\). Let’s try \(13,700\):
\(\begin{array}{lrrc}
\text { County } & \text { Population } & \text{ Quota } & \text{ Initial } \\
\hline \text { Bristol } & 49,875 & 3.6405 & 3 \\
\text { Kent } & 166,158 & 12.1283 & 12 \\
\text { Newport } & 82,888 & 6.0502 & 6 \\
\text { Providence } & 626,667 & 45.7421 & 45 \\
\text { Washington } & 126,979 & 9.2685 & 9\\
\textbf{ Total } & \bf{ 1,052,567 } & & \bf{ 75 }\end{array}\)
This works.
Notice, in comparison to Hamilton’s method, that although the results were the same, they came about in a different way, and the outcome was almost different. Providence County (the largest) almost went up to 46 representatives before Kent (which is much smaller) got to 12. Although that didn’t happen here, it can. Divisor-adjusting methods like Jefferson’s are not guaranteed to follow the quota rule!


19.10.1: Review Questions
Review Questions
Explain how parallax measurements can be used to determine distances to stars. Why can we not make accurate measurements of parallax beyond a certain distance?
2.
Suppose you have discovered a new cepheid variable star. What steps would you take to determine its distance?
3.
Explain how you would use the spectrum of a star to estimate its distance.
4.
Which method would you use to obtain the distance to each of the following?
- An asteroid crossing Earth’s orbit
- A star astronomers believe to be no more than 50 light-years from the Sun
- A tight group of stars in the Milky Way Galaxy that includes a significant number of variable stars
- A star that is not variable but for which you can obtain a clearly defined spectrum
5.
What are the luminosity class and spectral type of a star with an effective temperature of 5000 K and a luminosity of 100 L Sun ?


44.1: Median
Lesson
Let's explore the median of a data set and what it tells us.
Exercise \(\PageIndex{1}\): The Plot of the Story
- Here are two dot plots and two stories. Match each story with a dot plot that could represent it. Be prepared to explain your reasoning.
- Twenty people—high school students, teachers, and invited guests—attended a rehearsal for a high school musical. The mean age was 38.5 years and the MAD was 16.5 years.
- High school soccer team practice is usually watched by supporters of the players. One evening, twenty people watched the team practice. The mean age was 38.5 years and the MAD was 12.7 years.
-
Another evening, twenty people watched the soccer team practice. The mean age was similar to that from the first evening, but the MAD was greater (about 20 years).
Make a dot plot that could illustrate the distribution of ages in this story.
Exercise \(\PageIndex{2}\): Siblings in the House
Here is data that shows the numbers of siblings of ten students in Tyler’s class.
\(1\qquad 0\qquad 2\qquad 1\qquad 7\qquad 0\qquad 2\qquad 0\qquad 1\qquad 10\)
- Represent the data shown with a dot plot.
- Without making any calculations, estimate the center of the data based on your dot plot. What is a typical number of siblings for these sixth-grade students? Mark the location of that number on your dot plot.
- Find the mean. Show your reasoning.
-
- How does the mean compare to the value that you marked on the dot plot as a typical number of siblings? (Is it a little larger, a lot larger, exactly the same, a little smaller, or a lot smaller than your estimate?)
- Do you think the mean summarizes the data set well? Explain your reasoning.
Are you ready for more?
Invent a data set with a mean that is significantly lower than what you would consider a typical value for the data set.
Exercise \(\PageIndex{3}\): Finding the Middle
- Your teacher will give you an index card. Write your first and last names on the card. Then record the total number of letters in your name. After that, pause for additional instructions from your teacher.
- Here is the data set on numbers of siblings from an earlier activity.
\(1\qquad 0\qquad 2\qquad 1\qquad 7\qquad 0\qquad 2\qquad 0\qquad 1\qquad 10\)
- Sort the data from least to greatest, and then find the median .
- In this situation, do you think the median is a good measure of a typical number of siblings for this group? Explain your reasoning.
- Here is the dot plot showing the travel time, in minutes, of Elena’s bus rides to school.
- Find the median travel time. Be prepared to explain your reasoning.
- What does the median tell us in this context?
Summary
The median is another measure of center of a distribution. It is the middle value in a data set when values are listed in order. Half of the values in a data set are less than or equal to the median,and half of the values are greater than or equal to the median.
To find the median, we order the data values from least to greatest and find the number in the middle.
Suppose we have 5 dogs whose weights, in pounds, are shown in the table. The median weight for this group of dogs is 32 pounds because three dogs weigh less than or equal to 32 pounds and three dogs weigh greater than or equal to 32 pounds.
\(20\qquad 25\qquad 32\qquad 40\qquad 55\)
Now suppose we have 6 cats whose weights, in pounds, are as shown in the table. Notice that there are two values in the middle: 7 and 8.
\(4\qquad 6\qquad 7\qquad 8\qquad 10\qquad 10\)
The median weight must be between 7 and 8 pounds, because half of the cats weigh less or equal to 7 pounds and half of the cats weigh greater than or equal to 8 pounds.
In general, when we have an even number of values, we take the number exactly in between the two middle values. In this case, the median cat weight is 7.5 pounds because \((7+8)\div 2=7.5\).
Glossary Entries
Definition: Median
The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.
For the data set 7, 9, 12, 13, 14, the median is 12.
For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. \(6+8=14\) and \(14\div 2=7\).
Practice
Exercise \(\PageIndex{4}\)
Here is data that shows a student's scores for 10 rounds of a video game.
\(130\qquad 150\qquad 120\qquad 170\qquad 130\qquad 120\qquad 160\qquad 160\qquad 190\qquad 140\)
What is the median score?
- \(125\)
- \(145\)
- \(147\)
- \(150\)
Exercise \(\PageIndex{5}\)
When he sorts the class’s scores on the last test, the teacher notices that exactly 12 students scored better than Clare and exactly 12 students scored worse than Clare. Does this mean that Clare’s score on the test is the median? Explain your reasoning.
Exercise \(\PageIndex{6}\)
The medians of the following dot plots are 6, 12, 13, and 15, but not in that order. Match each dot plot with its median.
Exercise \(\PageIndex{7}\)
Invent a data set with five numbers that has a mean of 10 and a median of 12.
Exercise \(\PageIndex{8}\)
Ten sixth-grade students reported the hours of sleep they get on nights before a school day. Their responses are recorded in the dot plot.
Looking at the dot plot, Lin estimated the mean number of hours of sleep to be 8.5 hours. Noah's estimate was 7.5 hours. Diego's estimate was 6.5 hours.
Which estimate do you think is best? Explain how you know.
(From Unit 8.3.2)
Exercise \(\PageIndex{9}\)
In one study of wild bears, researchers measured the weights, in pounds, of 143 wild bears that ranged in age from newborn to 15 years old. The data were used to make this histogram.
- What can you say about the heaviest bear in this group?
- What is a typical weight for the bears in this group?
- Do more than half of the bears in this group weigh less than 250 pounds?
- If weight is related to age, with older bears tending to have greater body weights, would you say that there were more old bears or more young bears in the group? Explain your reasoning.
(From Unit 8.2.6)