5.3: Philosophical Perspective of Education
Essentialism
Perennialism
Progressivism
Social Reconstructionism & Critical Pedagogy
Contributors and Attributions
CC licensed content, Original
selected template will load here
This action is not available.
There are four philosophical perspectives currently used in educational settings: essentialism, perennialism, progressivism, and social reconstructionism/critical pedagogy. Unlike the more abstract ontology and axiology, these four perspectives focus primarily on what should be taught and how it should be taught, i.e. the curriculum.
Essentialism adheres to a belief that a core set of essential skills must be taught to all students. Essentialists tend to privilege traditional academic disciplines that will develop prescribed skills and objectives in different content areas as well as develop a common culture. Typically, essentialism argues for a back-to-basics approach on teaching intellectual and moral standards. Schools should prepare all students to be productive members of society. Essentialist curricula focuses on reading, writing, computing clearly and logically about objective facts about the outside real world. Schools should be sites of rigor where students learn to work hard and respect authority. Because of this stance, essentialism tends to subscribe to tenets of Realism. Essentialist classrooms tend to be teacher-centered in instructional delivery with an emphasis on lecture and teacher demonstrations.
Key theorists:
William Bagley, E.D. Hirsh Jr.
Perennialism advocates for seeking, teaching, and learning universal truths that span across historical time periods. These truths, Perennialists argue, have everlasting importance in helping humans solve problems regardless of time and place. While Perennialism resembles essentialism at first glance, perennialism focuses on the individual development of the student rather than emphasizing skills. Perennialism supports liberal arts curricula that helps produces well-rounded individuals with some knowledge across the arts and sciences. All students should take classes in English Language Arts, foreign languages, mathematics, natural sciences, fine arts, and philosophy. Like Essentialism, Perennialism may tend to favor teacher-centered instruction; however, Perennialists do utilize student-centered instructional activities like Socratic Seminar, which values and encourages students to think, rationalize, and develop their own ideas on topics.
Key theorists:
Robert Hutchins, Mortimer Adler
Progressivism focuses its educational stance toward experiential learning with a focus on developing the whole child. Students learn by doing rather than being lectured to by teachers. Curriculum is usually integrated across contents instead of siloed into different disciplines. Progressivism’s stance is in stark contrast to both Essentialism and Perennialism in this manner. Progressivism follows a clear pragmatic ontology where the learner focuses on solving real-world problems through real experiences. Progressivist classrooms are student-centered where students will work in cooperative/collaborative groups to do project-based, expeditionary, problem-based, and/or service-learning activities. In progressivist classrooms, students have opportunities to follow their interests and have shared authority in planning and decision making with teachers.
Key theorists:
John Dewey, Maria Montessori
Social reconstructionism was founded as a response to the atrocities of World War II and the Holocaust to assuage human cruelty. Social reform in response to helping prepare students to make a better world through instilling democratic values. Critical pedagogy emerged from the foundation of the early social reconstructionist movement. Critical pedagogy is the application of critical theory to education. For critical pedagogues, teaching and learning is inherently a political act and they declare that knowledge and language are not neutral, nor can they be objective. Therefore, issues involving social, environmental, or economic justice cannot be separated from the curriculum. Critical pedagogy’s goal is to emancipate marginalized or oppressed groups by developing, according to Paulo Freire, conscientização, or critical consciousness in students. Critical pedagogy de-centers the traditional classroom, which positions teacher at the center. The curriculum and classroom with a critical pedagogy stance is student-centered and focuses its content on social critique and political action.
Key theorists:
Paulo Freire, bell hooks (note: bell hooks intentionally does not capitalize her name, which follows her critical stance that language, even how we write one’s own name, is political and ideological.)


16.5: Prokaryotic Gene Regulation - The lac Operon- An Inducer Operon
- Describe the components of the lac operon and their role in its function
A major type of gene regulation that occurs in prokaryotic cells utilizes and occurs through inducible operons. Inducible operons have proteins that can bind to either activate or repress transcription depending on the local environment and the needs of the cell. The lac operon is a typical inducible operon. As mentioned previously, E. coli is able to use other sugars as energy sources when glucose concentrations are low. To do so, the cAMP–CAP protein complex serves as a positive regulator to induce transcription. One such sugar source is lactose. The lac operon encodes the genes necessary to acquire and process the lactose from the local environment, which includes the structural genes lacZ, lacY, and lacA. lacZ encodes β-galactosidase (LacZ), an intracellular enzyme that cleaves the disaccharide lactose into glucose and galactose. lacY encodes β-galactoside permease (LacY), a membrane-bound transport protein that pumps lactose into the cell. lacA encodes β-galactoside transacetylase (LacA), an enzyme that transfers an acetyl group from acetyl-CoA to β-galactosides. Only lacZ and lacY appear to be necessary for lactose catabolism.
CAP binds to the operator sequence upstream of the promoter that initiates transcription of the lac operon. The lac operon uses a two-part control mechanism to ensure that the cell expends energy producing β-galactosidase, β-galactoside permease, and thiogalactoside transacetylase (also known as galactoside O-acetyltransferase) only when necessary. However, for the lac operon to be activated, two conditions must be met. First, the level of glucose must be very low or non-existent. Second, lactose must be present. If glucose is absent, then CAP can bind to the operator sequence to activate transcription. If lactose is absent, then the repressor binds to the operator to prevent transcription. If either of these requirements is met, then transcription remains off. The cell can use lactose as an energy source by producing the enzyme b-galactosidase to digest that lactose into glucose and galactose. Only when both conditions are satisfied is the lac operon transcribed, such as when glucose is absent and lactose is present. This process is beneficial and makes most sense for the cell as it would be energetically wasteful to create the proteins to process lactose if glucose were plentiful or if lactose were not available.
Contributions and Attributions
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...ol11448/latest . License : CC BY: Attribution
- operon. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/operon . License : CC BY-SA: Attribution-ShareAlike
- repressor. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/repressor . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Prokaryotic Gene Regulation. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...e_16_02_01.jpg . License : CC BY: Attribution
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...ol11448/latest . License : CC BY: Attribution
- Catabolite activator protein. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Catabol...ivator_protein . License : CC BY-SA: Attribution-ShareAlike
- RNA polymerase. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/RNA%20polymerase . License : CC BY-SA: Attribution-ShareAlike
- operon. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/operon . License : CC BY-SA: Attribution-ShareAlike
- promoter. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/promoter . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Prokaryotic Gene Regulation. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...e_16_02_01.jpg . License : CC BY: Attribution
- OpenStax College, Prokaryotic Gene Regulation. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...e_16_02_02.jpg . License : CC BY: Attribution
- repressor. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/repressor . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Biology. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...ol11448/latest . License : CC BY: Attribution
- An Introduction to Molecular Biology/Gene Expression. Provided by : Wikibooks. Located at : en.wikibooks.org/wiki/An_Intr...ene_Expression . License : CC BY-SA: Attribution-ShareAlike
- operator. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/operator . License : CC BY-SA: Attribution-ShareAlike
- OpenStax College, Prokaryotic Gene Regulation. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...e_16_02_01.jpg . License : CC BY: Attribution
- OpenStax College, Prokaryotic Gene Regulation. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...e_16_02_02.jpg . License : CC BY: Attribution
- OpenStax College, Prokaryotic Gene Regulation. October 16, 2013. Provided by : OpenStax CNX. Located at : http://cnx.org/content/m44535/latest...e_16_02_03.png . License : CC BY: Attribution
Key Points
- The lac operon contains an operator, promoter, and structural genes that are transcribed together and are under the control of the catabolite activator protein (CAP) or repressor.
- The lac operon is not activated and transcription remains off when the level of glucose is low or non-existent, but lactose is absent.
- The lac operon encodes for the genes needed to utilize lactose as an energy source.
Key Terms
- operator : a segment of DNA to which a transcription factor protein binds
- repressor : any protein that binds to DNA and thus regulates the expression of genes by decreasing the rate of transcription


8.4: Storage Temperatures and Procedures
-
- Last updated
- Save as PDF
- BC Cook Articulation Committee
- BCcampus
A food service operation needs to have clearly defined storage areas and procedures for several reasons. First, by providing storage facilities it is possible to purchase supplies in quantities large enough quantities to get price breaks. Second, the ability to store supplies on the premises reduces the cost and time needed to order supplies and handle them upon delivery. Third, menu planning is easier when you are aware of the quality, quantity, and types of supplies that are on hand. If there is a run on a particular menu item, it is nice to know there are enough materials on hand to ensure that everyone who orders the item can be served.
In today’s market, many food service operations are reducing the amount of stock they keep on hand because storage is expensive. Not only does space need to be found but security needs to be tight. Many operators are willing to pay a bit extra to suppliers in order to avoid the headaches of keeping track of expensive items such as large quantities of high-quality meat, wines, and spirits.
Regardless, there still is a need for storing many types of supplies including dry foods, dairy products, frozen foods, produce, and fresh meats. Storage areas for such items often have design requirements that must be built into the space in order to efficiently handle the specific types of supplies.
Dry Foods
The storeroom for dry foods should be located near the receiving area and close to the main kitchen. Unfortunately, the storeroom for dry foods is often an afterthought in food service facility designs, and the area designated for storage is sometimes in an inconvenient location.
No matter where the location, there are several essential points to be observed in the care and control of the dry storeroom.
- The area should be dry and cool to prevent spoilage and the swelling of canned goods. The ideal temperature range is 50°F to 59°F (10°C to 15°C ).
- The storeroom should be easy to keep clean and free from rodents and vermin. This means all wall, ceiling, and floor openings should be sealed and protected to prevent access.
- It should be designed so it is easy to arrange and rearrange supplies to facilitate stock rotation. The best arrangement is to have shelves situated in the middle of the room so they can be stocked from both sides. This allows you to rotate stock by simply pushing out old stock by sliding new stock in from the other side of the shelf. This guarantees that first items received will be the first items used, or the “first in, first out” ( FIFO ) concept in stock rotation.
- The area should be well lit.
- Shelving must be at least 15 cm (6 in.) above the floor. Do not store items right on the floor.
- Aisles should be wide enough to allow room for carts or dollies, which should be used to prevent possible injuries from lifting.
- Food and supply storage areas should be kept under lock and key to prevent pilferage. Food storage control is an important step in the overall control of food costs. All storerooms should be considered to be like bank safes where the assets of the operation are being stored. This may mean that more valuable commodities such as liquor and wine should be stored and locked inside a larger storage area, such as the dry food storage area.
Refrigerated Products
The refrigerator, whether a walk-in or a standard upright, is an important component in planning the storage of food items. Most fresh foods must be stored in the refrigerator to delay their deterioration and decomposition. The most basic rule must be always followed: store raw products below, never above, your cooked or ready-to-eat products.
Critical Control Point
Keep foods 39°F (4°C) or colder, the safe temperature for refrigerated storage.
Here are some considerations to ensure that the refrigerator does not break down and risk spoiling food:
- Monitor the temperature of the refrigerator daily. All refrigerators should be provided with a thermometer so that daily readings can be taken.
- Keep refrigerators in good working order. Maintain a regular servicing contract with a local refrigerator repair company.
- Most breakdowns are beyond the ability of kitchen staff to repair, but if the refrigerator does stop running, first check that the power supply cord hasn’t simply been pulled out or the breaker has flipped off.
- Clean refrigerators regularly. Shelves should be shallow and well vented to make such cleaning quick and easy. Develop and follow a schedule to ensure that refrigerators are cleaned on a consistent basis.
There are also several general rules that all personnel using the refrigerator should follow:
- Store raw products below cooked or ready-to-eat products.
- Develop and follow a FIFO system for refrigerated food.
- Designate areas in the refrigerator for certain items, and keep only those items in their designated place.
- Never put hot foods in the refrigerator unless absolutely necessary. (Unfortunately, one person’s understanding of “necessary” may not be the same as another person’s, so consider developing guidelines.)
- Never leave the refrigerator door open longer than needed.
Although lack of time and personnel shortages often make it difficult to observe these rules, it is imperative that they be followed.
Dairy Products
Dairy products must be stored in the refrigerator at temperatures of 36° to 39°F (2°C to 4°C). Follow these guidelines:
- The fat in dairy products has a tendency to absorb strong odors from the storage surroundings. To reduce the likelihood of this happening, store dairy products in their own area in protective coverings.
- Do not store dairy products in a vegetable cooler; a separate refrigerator is much more acceptable.
- Keep the refrigerator clean at all times.
- Rotate dairy products when fresh product arrives. Dairy products should not be ordered too far in advance of when they will be used. Ideally, such products should be delivered on a daily basis.
Produce
Most produce is stored in the refrigerator at 36° to 39°F (2° to 4°C) to ensure freshness and to prevent rapid deterioration. There are, however, a number of exceptions, including potatoes and bananas, which should be stored at higher temperatures.
Keep these factors in mind when storing produce:
- Soft fruits should not be stored too long. It is often best to buy soft fruit as you need it, keeping very little on hand.
- Unripe fruit can be ripened at storeroom temperatures of 50°F to 59°F (10°C to 15°C). It will ripen much more slowly under refrigerator conditions.
- Before storing and when rotating stock, it is important to remove rotting fruit from cases as one piece can affect others. The chain reaction can quickly destroy the quality of a whole case of fruit.
- Be aware of special storage problems. For example, bananas stored in the refrigerator turn black quickly. Bananas should be stored under conditions where the temperature range is 50°F to 59°F (10°C to 15°C).
- The length of time produce can be stored varies widely. For example, hardy vegetables such as carrots and cabbage will last for weeks, while delicate vegetables such as lettuce should be bought as fresh as possible as they do not keep for long.
- Moisture on vegetables tends to soften them, causing rot. Even though in the early stages of rot there is nothing basically wrong with such vegetables, they can be unattractive to the eye.
Fresh Meats, Poultry, and Seafood
These items are the most difficult to store and the most expensive food items sold by the restaurant. When storing meats, poultry, and seafood items, remember the critical control point.
Critical Control Point
Keep foods 39°F (4°C) or colder, the safe temperature for refrigerated storage.
Keep these factors in mind when storing fresh meats, poultry, and produce:
- All carcass meats should be unwrapped and hung so that air can circulate around them. They should be stored at 34°F to 37°F (1°C to 3°C) in a walk-in refrigerator. Place absorbent paper under the meats for quick cleanup of any unwanted drips.
- Fresh meat must not be kept too long. Boned meat should be kept no longer than three days. Individual cuts should be used within two days, preferably on the day they are cut.
- Individual meat cuts such as steaks, chops, stewing meat, and ground meat should be kept covered on plastic or stainless steel trays at 36°F to 39°F (2°C to 4°C).
- Fresh poultry should be packed in ice and stored in the refrigerator.
- Fresh seafood should be packed in ice, stored at 30°C to 34°F (−1°C to 2°C) and used as soon as possible.
- Store raw products on the lower shelves of the refrigerator, below cooked products.
Frozen Foods
Frozen foods should be stored at 0°F (–18°C) or lower. If the temperature rises above 0°F, food can become discolored and lose vitamin content. Lowering the temperature after it has risen does not correct the damage.
Critical Control Point
Frozen food must be kept at 0°F or lower to maintain its quality.
Keep these factors in mind when storing frozen foods:
- Fruit and vegetables that are received frozen will keep for months if they are properly wrapped. Fish and meat properly wrapped also have a relatively long freezer shelf life.
- Freezing fresh fruits and vegetables on the premises is time consuming and may be too expensive to consider. Fresh fruit must be properly prepared for freezing or it will not store well.
- All freezer products not properly wrapped will develop freezer burn, which is a loss of moisture that affects both the texture and the flavor of the food.  Meat is particularly susceptible to freezer burn.
- Rotating stock is extremely important with frozen foods. Such rotation is difficult in standard chest freezers as it often means that old stock must be removed before new stock is added. The temptation with frozen foods is to develop the unacceptable habit of using the last item bought first, instead of FIFO (first in, first out).


10.2: Google Plus
Describe the primary use of Google Plus
Google Plus (also written as Google+) is Google’s answer to Facebook. Using very similar features, Google Plus integrates (naturally) very well into other Google services, especially YouTube. While it never caught on the way Facebook has—its usage is relatively low at 111 million versus Facebook’s 2.07 billion—it has elegant tools, many of which could be used for various business-communication purposes.
Perhaps the most useful feature of Google Plus is the Communities tool. This tool brings users together around a given theme, such as, “home education in California,” and then allows people to connect and interact around that theme. It is similar to Facebook’s Groups feature.
When assessing the usefulness of Google Plus, you should keep the pros and cons listed in Table 1 in mind:
| Table 1. Pros and Cons of Google Plus as a Social Media Platform | |
|---|---|
| Pros | Cons |
| Potential for large audience (integration with other Google services) | Never caught on like Facebook; relatively low usage |
| Created local search engine optimization (SEO) | More manual work to integrate with other social media platforms (minus YouTube) |
Contributors and Attributions
- Google Plus. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- How to Use Google+ Plus for Beginners. Authored by : Yeah Likes. Located at : https://youtu.be/c25g9oSHdsc . License : All Rights Reserved . License Terms : Standard YouTube License


7.1: History and Demographics
-
- Last updated
- Save as PDF
- Erika Gutierrez, Janét Hund, Shaheen Johnson, Carlos Ramos, Lisette Rodriguez, & Joy Tsuhako
- Long Beach City College, Cerritos College, & Saddleback College via ASCCC Open Educational Resources Initiative (OERI)
African Americans: How and Why They Came
The term African American can be a misnomer for many individuals. African Americans (also referred to as Black Americans) are a race-ethnic group of Americans with total or partial ancestry from any of the Black racial groups of Africa. The term African American generally denotes descendants of enslaved Black people who are from the United States, while some recent Black immigrants or their children may also come to identify as African-American or may identify differently.
African Americans are the largest race-ethnic group behind Euro Americans (whites) and Latinx. Most African Americans are descendants of enslaved peoples within the boundaries of the present United States. On average, African Americans are of West/Central African and European descent, and some also have Native American ancestry. According to U.S. Census Bureau data, African immigrants generally do not self-identify as African American. The overwhelming majority of African immigrants identify instead with their own respective ethnicities. This section will focus on the experience of Africans who were captured, enslaved and transported from Africa to the United States, and their offspring.
If Native Americans are the only minoritized group whose subordinate status occurred by conquest, African Americans are the exemplar minority group in the United States whose ancestors did not come here by choice. A Dutch sea captain brought the first Africans to the Virginia colony of Jamestown in 1619 and sold them as indentured servants. This was not an uncommon practice for either Blacks or whites, and indentured servants were in high demand. For the next century, Black and white indentured servants worked side by side. But the growing agricultural economy demanded greater and cheaper labor, and by 1705, Virginia passed the slave codes declaring that any foreign-born non-Christian could be a slave, and that slaves were considered property.
The next 150 years saw the rise of U.S. slavery, with Black Africans being kidnapped from their own lands and shipped to the New World on the trans-Atlantic journey known as the Middle Passage. Once in the Americas, the Black population grew until U.S.-born Blacks outnumbered those born in Africa. But colonial (and later, U.S.) slave codes declared that the child of a slave was a slave, so the slave class was created.
Justification for African Slavery
Skin color was an instrument of justifying slavery in the Americas. The Portuguese and the Spanish were among the first to bring African slaves to the Americas. In 1542, the enslaving of Indigenous peoples in its New World territories was made illegal by the government of Spain, an action that greatly expanded and facilitated the primary use of Africans in the trans-Atlantic slave trade in North America. As David Brion Davis (2008) stated, “It was not until the seventeenth century that...New World slavery began to be overwhelmingly associated with people of Black African descent.” According to Nathan Rutstein (1997), “In all of the original 13 colonies, there was the prevailing belief among whites that the Caucasian race was not only superior to the African races, but that Africans were part of a lower species, something between the ape and the human.”
It is perhaps difficult to comprehend how the United States, founded on the principles of liberty, democracy and Christian values, could establish a system as inhumane as slavery. It becomes more understandable with the historical context that Black skin and slavery were considered to be a curse from God. Although slavery was driven by economic need, race and theology were used to justify it. According to Goldenberg (2017), the Bible was used as justification for slavery: “...the Bible...consigned Blacks to everlasting servitude...[and] provided biblical validation for sustaining the slave system.” David Brion Davis (2008)has written extensively about the impact of the Curse of Ham on slavery and attitudes toward African Americans in the antebellum era. He stated that “the ‘Curse of Ham’ was repeatedly used as the most authoritative justification for ‘Negro slavery’ by nineteenth-century Southern Christians, by many Northern Christians, and even by a few Jews” (Davis, 2008).
This section licensed CC BY-NC. Attribution: Slavery to Liberation: The African American Experience (Encompass) ( CC BY-NC 4.0 )
The Curse of Ham
Perhaps the most significant influence on universal attitudes and negative perceptions of people of color is the biblical story of the “Curse of Ham” found in the King James Version (1611) of the Bible in Genesis 9:18-27. The event occurs after Noah and his three sons and their families have left the ark after the Great Flood. Noah’s three sons were Shem, Ham, and Japheth. One day, Noah became drunk from wine made from grapes grown in his vineyard. He fell asleep nude on the floor in his tent. Ham’s two brothers, Shem and Japheth, turned away and did not view their father’s naked body. Ham refused to turn away and saw Noah drunk and naked. Shem and Japheth took a garment, put it on their shoulders, and backed into the tent. They covered Noah with the garment without looking at their father’s nude body. After Noah later awoke and became aware of what Ham had done, he pronounced the biblical curse, "Cursed be Canaan; the lowest of slaves shall he be to his brothers."
 Noah then blessed Ham’s two brothers, Shem and Japheth. It was after this event that the three sons of Noah went with their families to populate the entire earth. Canaan and his family traveled to settle in the area of the world that is now the continent of Africa. One of Ham’s brothers (Japheth) went to settle in the area that is now Europe, and the other brother (Shem) went to settle with his family in the area known as Asia.
Noah’s statement that Canaan would be the “lowest of slaves” to his two brothers became universally interpreted as an eternal affliction of servitude by God. The Curse of Ham was widespread throughout Europe and eventually spread to America. The Christian Bible does not mention skin color in the story of Noah’s curse, but the conflating of Black skin color with the punishment of eternal servitude later became combined with the original biblical interpretation of the Curse of Ham. The text of the biblical story was translated over centuries by Muslim, Jewish, and Christian writers.
Black Identity
Findings from Pew Research Center surveys conducted in recent years show that most Black adults feel that they are part of a broader Black community in the United States and see their race as important to how they think of themselves. As conveyed in Figure 7.1.2, about three-quarters of Black adults say that being Black is extremely (52%) or very (22%) important to how they think about themselves, according to a 2019 Pew Research Center survey .
In addition, a Pew Research Center survey conducted in 2016 reveals that most Black adults (81%) said they felt at least somewhat connected to a broader Black community in the U.S., including 36% who said they felt very connected to a Black community, as shown in Figure 7.1.3
As presented in Figure 7.1.4, Black adults who said they feel strongly connected to a broader Black community are more likely (than those who don’t have such connections) to have engaged with organizations such as the NAACP, Urban League, Black Lives Matter and Black Greek Fraternities/Sororities dedicated to improving the lives of Black Americans by donating money, attending events or volunteering their time.
Black Demographics
Between the end of the Civil War and the beginning of the Great Depression, nearly two million African Americans fled the rural South to seek new opportunities elsewhere. While some moved west, the vast majority of this Great Migration , as the large exodus of African Americans leaving the South in the early twentieth century was called, traveled to the Northeast and Upper Midwest. The following cities were the primary destinations for these African Americans: New York, Chicago, Philadelphia, St. Louis, Detroit, Pittsburgh, Cleveland, and Indianapolis. These eight cities accounted for over two-thirds of the total population of the African American migration.
A combination of both “push” and “pull” factors played a role in this movement. Despite the end of the Civil War and the passage of the Thirteenth, Fourteenth, and Fifteenth Amendments to the U.S. Constitution (ensuring freedom, the right to vote regardless of race, and equal protection under the law, respectively), African Americans were still subjected to intense racial hatred. The rise of the Ku Klux Klan in the immediate aftermath of the Civil War led to increased death threats, violence, and a wave of lynchings. Even after the formal dismantling of the Klan in the late 1870s, racially motivated violence continued. According to researchers at the Tuskegee Institute, there were thirty-five hundred racially motivated lynchings and other murders committed in the South between 1865 and 1900. For African Americans fleeing this culture of violence, northern and midwestern cities offered an opportunity to escape the dangers of the South.
In addition to this “push” out of the South, African Americans were also “pulled” to the cities by factors that attracted them, including job opportunities, where they could earn a wage rather than be tied to a landlord, and the chance to vote (for men, at least), supposedly free from the threat of violence. Although many lacked the funds to move themselves north, factory owners and other businesses that sought cheap labor assisted the migration. Often, the men moved first then sent for their families once they were ensconced in their new city life. Racism and a lack of formal education relegated these African American workers to many of the lower-paying unskilled or semi-skilled occupations. More than 80 percent of African American men worked menial jobs in steel mills, mines, construction, and meat packing. In the railroad industry, they were often employed as porters or servants (Figure 7.1.5). In other businesses, they worked as janitors, waiters, or cooks. African American women, who faced discrimination due to both their race and gender, found a few job opportunities in the garment industry or laundries, but were more often employed as maids and domestic servants. Regardless of the status of their jobs, however, African Americans earned higher wages in the North than they did for the same occupations in the South, and typically found housing to be more available.
However, such economic gains were offset by the higher cost of living in the North, especially in terms of rent, food costs, and other essentials. As a result, African Americans often found themselves living in overcrowded, unsanitary conditions, much like the tenement slums in which European immigrants lived in the cities. For newly arrived African Americans, even those who sought out the cities for the opportunities they provided, life in these urban centers was exceedingly difficult. They quickly learned that racial discrimination did not end at the Mason-Dixon Line, but continued to flourish in the North as well as the South. European immigrants, also seeking a better life in the cities of the United States, resented the arrival of the African Americans, whom they feared would compete for the same jobs or offer to work at lower wages. Landlords frequently discriminated against them; their rapid influx into the cities created severe housing shortages and even more overcrowded tenements. Homeowners in traditionally white neighborhoods later entered into covenants in which they agreed not to sell to African American buyers; they also often fled neighborhoods into which African Americans had gained successful entry. In addition, some bankers practiced mortgage discrimination, later known as “redlining,” in order to deny home loans to qualified buyers. Such pervasive discrimination led to a concentration of African Americans in some of the worst slum areas of most major metropolitan cities, a problem that remained ongoing throughout most of the twentieth century.
So why move to the North, given that the economic challenges they faced were similar to those that African Americans encountered in the South? The answer lies in noneconomic gains. Greater educational opportunities and more expansive personal freedoms mattered greatly to the African Americans who made the trek northward during the Great Migration. State legislatures and local school districts allocated more funds for the education of both Blacks and whites in the North, and also enforced compulsory school attendance laws more rigorously. Similarly, unlike the South where a simple gesture (or lack of a deferential one) could result in physical harm to the African American who committed it, life in larger, crowded northern urban centers permitted a degree of anonymity—and with it, personal freedom—that enabled African Americans to move, work, and speak without deferring to every white person with whom they crossed paths. Psychologically, these gains more than offset the continued economic challenges that Black migrants faced.
The Migrating U.S. Black Population
Although, the Black share of the total U.S. population has not changed substantially over the last two decades, the number of majority Black counties in the U.S. grew from 65 to 72 between 2000 and 2018. One contributing factor may be migration of Black Americans from the North to the South and from cities into suburbs. According to Pew Research, there are now 15 majority Black counties that were not majority Black in 2000. Among them, Rockdale County, Georgia, located about half an hour outside Atlanta, had the largest percentage point increase in the share of Black residents (from 18% in 2000 to 55% in 2018). With about 930,000 residents, Shelby County, Tennessee, which contains Memphis, was the county with the largest population to become majority Black.
Meanwhile, eight counties that were majority Black in 2000 are no longer. Three of these are large U.S. cities that the Census Bureau includes in its county estimates: Washington, D.C.; Richmond, Virginia; and St. Louis, Missouri. Washington (home to roughly 702,000 residents in 2018) saw a 19% increase in total population during that period, while its Black population decreased by 9%. The city’s share of Black residents declined by 15 percentage points, from 60% to 45%.
Black immigrant population has increased fivefold since 1980 . Immigrants are making up a growing number of the overall U.S. population – but the Black immigrant population is growing twice as fast. As prestented in Figure 7.1.7, there were 4.2 million Black immigrants living in the U.S. in 2016, up from 816,000 in 1980, according to a Pew Research Center analysis of U.S. Census data. Since 2000 alone, the number of Black immigrants in the U.S. has risen 71%.
According to the Pew Research Center, much of the recent growth in the Black immigrant population has been fueled by African migration. Africans made up 39% of the overall Black immigrant population in 2016, up from 24% in 2000. Still, about half of all foreign-born Blacks (49%) living in the U.S. in 2016 were from the Caribbean.
Did You Know?
- 47.8 million The Black population, either alone or in combination with one or more races, in the United States in 2018.
- 87.9% The percentage of African-Americans age 25 and older with a high school diploma or higher in 2018.
- 29.9% The percentage of the employed Black population age 16 and older working in management, business, science and arts occupations in 2018.
- 121,466 The number of Black-owned employer businesses in the United States in 2016.
- 2.2 million The number of Black military veterans in the United States nationwide in 2018.
Source: United States Census Bureau, 2019.
Contributors and Attributions
Content on this page has multiple licenses. Everything is CC BY-SA other than Justification for African Slavery which is CC BY-NC.
- Johnson, Shaheen. (Long Beach City College)
- Hund, Janét. (Long Beach City College)
- Slavery to Liberation: The African American Experience (Encompass) ( CC BY-NC 4.0 ) (Contributed to Justification for African Slavery)
- The African American “Great Migration” and New European Immigration (OER Commons) ( CC BY-SA 4.0 )
- Introduction to Sociology 2e (OpenStax) ( CC BY 4.0 )
- African Americans (Wikipedia) ( CC BY-SA 3.0 )
Works Cited
- American FactFinder. (2011 June). United States - QT-P4. race, combinations of two races, and not Hispanic or Latino: 2000. United States Census.
- Davis, D.B. (2008). Inhuman Bondage: The Rise and Fall of Slavery in the New World. London, UK: Oxford University Press.
- Forson, T.S. (2018, February 21). Who is an 'African American'? definition evolves as USA does. USA Today .
- Goldenberg, D.M. (2017). Black and Slave: The Origins and History of the Curse of Ham. Berlin/Boston, MA: De Gruyter.
- Gomez, M.A. (1998). Exchanging Our Country Marks: The Transformation of African Identities in the Colonial and Antebellum South. Chapel Hill, NC: University of North Carolina.
- Locke, D.C., Bailey, D.F. (2013). Increasing Multicultural Understanding. Thousand Oaks, CA: SAGE Publications.
- Marable, M., Frazier, N., & McMillian, J.C. (2003). Freedom on My Mind: The Columbia Documentary History of the African American Experience. Boston, MA: Bedford/St. Martin’s.
- Martin C.L., & Fabes, R. (2008). Discovering Child Development. Boston, MA: Cengage Learning.
- Pe w Research Center. (2014). Religious tradition by race/ethnicity.
- Pew Research Center. (2019). The role of race and ethnicity in Americans' personal lives.
- Rutstein, N. (1997). Racism: Unraveling the Fear. Washington, DC: Global Classroom.
- United States Census Bureau . (2019, December). American community survey demographic and housing estimates.
- United States Census Bureau. (2020 January). Facts for features: national African-American (Black) history month: February 2020.
- United States Census Bureau. (2011 September). The Black population: 2010.
- U.S. Legal. (2021). African Americans law & legal definition.
- West, C. (1985). The paradox of afro-american rebellion. In S. Sayres (Ed), The 60s Without Apology. Minneapolis, MN: University of Minnesota Press. pp. 44-58.


13: Hypothesis Test for a Population Mean Given Statistics
Hypothesis Test for a Population Mean given Statistics
This calculator performs the hypothesis test for a population mean given statistics. Please report the error to Dr. Jessica Kuang at jkuangATvcccd.edu.
To learn how to use this calculator, please watch a short video here.
Input
Select if the population standard deviation, \(\sigma\), is known or unknown. Then fill in the sample size (\(n\)), the sample mean (\(\bar{x}\)), the standard deviation ( \(s\) ), the hypothesized population mean \(\mu_0\), and indicate if the test is left tailed (<), right taile (>), or two tailed ( \(\neq\) ), then click Calculate.
| Sample Size (\(n\)): |
| Sample Mean (\(\bar{x}\)): |
Choose the test \(\lt\) \(\gt\) \(\neq\) |
Hypothesized Population Mean (\(\mu_0\)): |
Output
(Powered by DESMOS)


28.3: Quick Tips for Evaluating Health Websites
Content on the Internet is unregulated; anyone can publish anything on the Internet. There is sound medical information on the Internet along with dangerous information. You need to be able to tell the difference.
Ask yourself the following:
- Why did the person create the page?
- What’s in it for them?
- Are they trying to sell me something?
Criteria for evaluating information from the web:
Accuracy
- Is the information based on sound medical research? Can the information on the web page be verified by another source?
- Are the sources cited reliable?
- Are there grammatical and spelling errors?
- Are there footnotes, bibliographies, or references so that you can verify the information? Are these reliable? (a citation to Parade magazine does not have the same weight as an article from JAMA )
Authority
- Who published the page? What are the person’s credentials? What do you know about them?
- Is the person backed by a known organization? (the American Association for Cancer Therapy may be a made-up name for something operating out of someone’s basement.)
- Is the person affiliated with a university? If so, is the person a student or a faculty member?
- Can you easily find contact information on the web page? Check the “about us” link, usually found at the beginning or the end of a webpage. What does the “About Us” section tell you about the purpose of the organization? Can you find a physical location for the organization? Or is the only way to contact the organization through a webform?
- What is the domain name? (.edu, .gov ) Is it a personal page or supported by the organization? The tilde (~) means that the site is a personal page (compare an address like med.harvard.edu/~jsmith/headache to med.harvard.edu/neurology/headache)
Bias/Objectivity
- Is the information showing just one point of view?
- What kind of institution sponsored the webpage? A pharmaceutical company? A non-profit organization?
- Is advertising clearly marked?
- Can you tell if the information you are reading is advertisement?
- Do the graphics, fonts, and verbiage play upon emotions? Beware of CAPITAL LETTERS, EXCLAMATION POINTS!!!!! Or words like MIRACLE CURE!!!
- Is the author using data improperly to promote a position or a product?
Currency/Timeliness
- Is there a date on the page?
- When was the page last updated?
- Do the links work?
- Has there been more recent research on the subject? Many medical treatments change with the publication of new studies. What was published a year ago may be outdated now.
Coverage
- Is the information complete?
- Are there sources given for additional information?
Additional Resources
MedlinePlus Guide to Healthy Web Surfing
http://www.nlm.nih.gov/medlineplus/healthywebsurfing.html
Trust It or Trash It? (evaluation tool)
Trust It or Trash It? (printer-friendly handout)
- Evaluating Health Websites. Authored by : National Network of Libraries of Medicine (link is no longer active). Provided by : National Institutes of Health. Located at : https://nnlm.gov/outreach/consumer/evalsite.html . License : Public Domain: No Known Copyright


2.7: Future Geographies- Feedbacks Driving Global Warming and Environmental Change
In this chapter we have learned that there are two types of feedbacks, positive feedbacks that drive system change and negative feedbacks that seek to keep systems in a state of equilibrium. Geoscientists like physical geographers are recognizing that positive feedback mechanisms may drive the Earth system past thresholds and towards a new state of equilibrium. In so doing, the distribution of climates and ecosystems may be irreversibly altered and a new physical geography of the Earth system will appear.
Examples of Feedbacks Driving Global Warming
Rising temperatures are expected to cause increased evaporation of water into the atmosphere, most of which will originate from oceans. The additional water vapor boosts the absorption of infrared radiation emitted by the earth resulting in more warming (a positive feedback). The increased warmth promotes more evaporation yielding an enhanced greenhouse effect. However, the addition of water may cause an increase in cloud cover resulting in a higher atmospheric albedo and reflection of incoming solar radiation. If this were to occur, the reduction in insolation would lead to cooling. Such contradictory consequences makes it difficult to determine what actually will occur in the future.
Throughout history, humans have cut forests to build structures, warm their homes, and cook their meals, and clear the land for agriculture. Removing forests removes a powerful sink for carbon dioxide. Leaving more CO 2 in the atmosphere enhances global warming and thus an increase in temperatures. As a result, temperature conditions that may be too warm to support healthy forest ecosystems. With less vegetation present, more carbon dioxide is left in the atmosphere causing more warming, another positive feedback driving the earth system toward ever warmer conditions. As temperatures increase, evaporation increases causing drier conditions and the threat of wildfires and forest destruction.
Geoscientists agree that the Arctic has been and will continue to be significantly impacted by global warming. Much of the land surface in the Arctic is underlain by permanently frozen ground called "permafrost". They uppermost "active layer" experiences seasonal thawing. Recent studies indicate that climatic warming my result in in a 12 to 15% reduction in the area covered by permafrost and a 15 to 30% increases in the thickness of the active layer. As temperature rises permafrost melts, releasing stored carbon, but just as importantly, methane. Increased warming results in more permafrost melting pushing the earth system ever forward into a future enhanced greenhouse environment.
Changes in Arctic ecosystems has already occurred as a result of global warming. Figures \(\PageIndex{3}\) a & b show two photographs from the same location in Alaska, showing the transition from tundra to wetlands over the last twenty years. When permafrost melts, water collects in small ponds on the surface increasing the heat gain nearly ten-fold. The additional heat continues to melt the underlying permafrost causing it to collapse and increasing the size of the pond. This positive feedback further degrades the permafrost.
As noted earlier in this chapter, carbon dioxide makes up a greater proportion of the atmosphere by volume, but methane absorbs energy much more efficiently. Increased warming at high latitudes may cause an increase in the release of methane from bogs or peatlands. Methane release from organic decomposition in wetlands coupled with carbon dioxide from melting permafrost will drive greenhouse gas levels higher, creating warmer temperatures.
Changes to the reflectivity of the surface (called the albedo) affects the amount of solar radiation absorb by the Earth. As Arctic sea ice melts it exposes open water which is less reflective (albedo decreases). The reduction in albedo allows more light to be absorbed by the ocean. As the ocean water warms, more heat is added to the air creating a positive feedback and driving Arctic temperatures ever higher. The reduction in sea ice is having a significant impact on arctic ecosystems.
Tipping Points and Environmental Change
Positive feedbacks drive the physical environment towards new physical states. In June of 2008, twenty years after his landmark testimony about global warming, NASA scientist Dr. James Hansen reiterated his warnings before the U.S. Congress. He cited several examples of earth systems reaching or nearing a tipping point. A
tipping level
(
point
) is a level at which "no additional forcing is required for large climate change and impacts." (Hansen, 2008). According to Hansen, a "point of no return" is reached when unstoppable and irreversible (on a practical time scale) occurs. A
tipping element
is a part of the earth system that has a tipping point, e.g., Arctic sea-ice loss, Sahara greening, Boreal forest dieback, permafrost and tundra loss. There is no one tipping point for the earth system as each element has its own point at which irreversible change will occur. For example, geoscientists believe that disintegration of the Greenland ice cap could occur if global temperature rises more than 2
o
C (3.6
o
F). For Arctic sea ice, the tipping point could occur with a rise of global mean temperature between .5
o
C (.9
o
F) to 2
o
C (3.6
o
F). Given the current amount of global warming, Arctic sea ice may have reached its tipping point.
Time is also an important factor in assessing whether a tipping point has been reached or a point of no return. Some, like Josefino Comiso of the NASA Goddard Space Flight Center, feel that the tipping point for perennial Arctic sea ice has already passed (National Geographic, 2007). David Barber, of the University of Manitoba is projecting that the North Pole will be ice free for the first time in history. For example, sea ice may completely disappear from the Arctic Ocean during the summer in a few years. This would represent a new state for the Arctic ocean. But temperature conditions could change in the relatively near future to permit sea ice to reform during the summer.
Assess you basic understanding of the preceding material by "Looking Back: Biogeochemical Cycles and Future Geographies" or skip and continue reading.


6.8: The Basics of Loans
- Describe various reasons for loans.
- Describe the terminology associated with loans.
- Understand how credit scoring works.
- Calculate the payment necessary to pay off a loan.
- Read an amortization table.
- Determine the cost to finance for a loan.
New car envy is real. Some people look at a new car and feel that they too should have a new car. The search begins. They find the model they want, in the color they want, with the features they want, and then they look at the price. That’s often the point where the new car fever breaks and the reality of borrowing money to purchase the car enters the picture. This borrowing takes the form of a loan.
In this section, we look at the basics of loans, including terminology, credit scores, payments, and the cost of borrowing money.
Reasons for Loans
Even if you want a new car because you need one, or if you need a new computer since your current one no longer runs as fast or smoothly as you would like, or you need a new chimney because the one on your house is crumbling, it’s likely you do not have that cost in cash. Those are very large purchases. How do you buy that if you don ’t have the cash?
You borrow the money.
And for helping you with your purchase, the company or bank charges you interest.
Loans are taken out to pay for goods or services when a person does not have the cash to pay for the goods or services. We are most familiar with loans for the big purchases in our lives, such as cars, homes, and a college education. Loans are also taken out to pay for repairs, smaller purchases, and home goods like furniture and computers.
Loans can come from a bank, or from the company selling the goods or providing the service. The borrower agrees to pay back more than the amount borrowed. So there is a cost to borrowing that should be considered when deciding on a purchase bought with credit or a borrowed money.
Even using a credit card is a form of a loan.
Essentially, a loan can be obtained for just about any purchase, large or small, that has a cost beyond a person’s cash on hand.
The Terminology of Loans
There are many words and acronyms that get used in relation to loans. A few are below.
APR is the annual percentage rate. It is the annual interest paid on the money that was borrowed. The principal is the total amount of the loan, or that has been financed. A fixed interest rate loan has an interest rate that does not change during the life of the loan. A variable interest rate loan has an interest rate that may change during the life of the loan. The term of the loan is how long the borrower has to pay the loan back. An installment loan is a loan with a fixed period, and the borrower pays a fixed amount per period until the loan is paid off. The periods are almost uniformly monthly. Loan amortization is the process used to calculate how much of each payment will be applied to principal and how much is applied to interest. Revolving credit , also known as open-end credit, is how most credit cards work but is also a kind of loan account. (We will learn about credit cards in Credit Cards) You can use up to some specified value, called the limit, any way you want, and as long as you pay the issuer of the credit according to their terms, you can keep borrowing from this account.
These and other terminologies can be researched further at Forbes .
Not everyone pays the same interest for the same loan. One person might get an APR of 2.9% while another pays 6.9%. These rates are based on your credit score.
Data about you and your credit is collected by three credit bureaus—Experian, Equifax, and TransUnion. They calculate your score using one of two main models: FICO and Vantage Score. The score they develop is based on the following categories:
- Payment History: Making your payments on time and not missing payments is by far the most important factor. All three credit types—revolving, installment, and open—contribute to this factor.
-
Credit Utilization or Amount Owed:
How much do you owe on your credit card accounts? This category is concerned with the ratio of how much you owe on revolving credit accounts relative to your available credit, also known as your credit utilization ratio.
This is the only category that depends solely on your revolving credit accounts. - Length of Credit History: This is the average age of your credit history, including the age of the oldest and newest accounts. All three types of credit accounts play a role in this category.
- Credit Mix: This number represents the different types of credit accounts you have, such as credit cards, car loan, mortgages, and whether you are successful managing both revolving and installment accounts.
- New Credit: Have you recently opened a new account or applied for new credit? Lenders want to know how much new credit you are taking on. So, if you are planning to buy a car and make another large purchase with a credit card, you may want to space these purchases out.
If you have done well in these categories, your credit score will be high, and you will qualify for lower interest rates because you are not perceived as being a risky investment. However, if you do poorly in these categories, your score will be low and you will pay higher interest rates since you present a greater risk.
Check out this nerdwallet article on credit scores to learn more!
Credit Scores Explained
There are many factors that impact your interest rate beyond your credit score. Banks have the authority to set their own rates, so competition between banks impacts interest rates. Bank A doesn’t want to charge interest rates that are too high, since borrowers will find banks with better rates. Banks also don’t want to charge too little interest.
The too little interest is more involved than the too high. The bank needs to make a profit on its loans. Deposits at the bank are used by the bank to generate loans. The bank has to pay those depositors interest. The bank must charge more for loans they give than they pay to people with deposits in the bank.
Banks also borrow money from each other. These loans have an interest rate, and once more, the bank making a loan must make a profit. More directly, they must charge more for loans they give than they pay for loans they take. In the United States, banks may also borrow from the Federal Reserve, which also charges an interest rate, which is also called the discount rate.
This is where a bank’s prime rate comes from. A bank’s prime rate is the interest rate it will give to its very best customers, which means most customers will pay more than the bank’s prime rate. To confuse the issue, there is also the Wall Street Journal ’s prime rate. It is the average of the prime rates charged by individual banks. The Wall Street Journal surveys several banks to generate this value.
Banks also increase the interest rate charged to customers based on both the credit risk presented by the customer, and the risk associate with what the loan will be used for.
Calculating Loan Payments
Loan payments are made up of two components. One component is the interest that accrued during the payment period. The other component is part of the principal. This should remind you of partial payments from Simple Interest.
Over the course of the loan, the amount of principal remaining to be paid decreases. The interest you pay in a month is based on the remaining principal, just as in the partial payments of Simple Interest.
The amount of interest, , to be paid for one period of a loan with remaining principal is , where is the interest rate in decimal form and is he number of payments in a year (most often = 12). Since the interest is for the one period, the time is 1 and does not impact the calculation. Note, interest paid to lenders is always rounded up to the next penny.
Find the interest to be paid for the period on loans with the following remaining principal and given annual interest rate. Each period is a month.
- Remaining principal is $13,450, interest rate is 6.75%
- Remaining principal is $8,460, interest rate is 5.99%
- Answer
-
- Substituting $13,450 for the remaining principal , 0.0675 for , and = 12 since the period is a month into the formula, we find that the interest to be paid this period is .
- Substituting $8,460 for the remaining principal , 0.0599 for , and = 12 since the period is a month into the formula, we find that the interest to be paid this period is .
Find the interest to be paid for the period on loans with the following remaining principal and given annual interest rate. Each period is a month.
Remaining principal is $56,945, interest rate is 7.5%
Remaining principal is $25,850, interest rate is 2.9%
The payment of the loan has to be such that the principal of the loan is paid off with the last payment. In any period, the amount of interest is defined by the formula above, but changes from period to period since the principal is decreasing with each payment. The trick is knowing how much principal should be paid each payment so that the loan is paid off at the stated time. Fortunately, that is found using the following formula.
The payment, , per period to pay down a loan with beginning principal is , where is the annual interest rate in decimal form, is the number of years of the loan, and is the number of payments per year (typically, loans are paid monthly making = 12).
Note, payment to lenders is always rounded up to the next penny.
Often, the formula takes the form , where is the interest rate per period (annual rate divided by the number of periods per year), and is the total number of payments to be made.
In the following, calculate the payment necessary to pay off the loan with the given details. The payments are monthly.
- A car loan taken out for $28,500 at an annual interest rate of 3.99% for 5 years.
- A home loan taken out for $136,700 and an annual interest rate of 5.75% for 15 years.
- Answer
-
-
The loan is for $28,500, which is the principal. The rate is 3.99%, so
= 0.0399. The term of the loan is 5 years, so
=5. Monthly payments means
= 12. Substituting these values for
,
,
, and
into the formula
and calculating, we find the payment for the loan.
The monthly payment needed is $524.75. -
The loan is for $136,000, which is the principal
. The rate is 5.75% so
= 0.0575. The term of the loan is 15 years, so
= 15. Monthly payments mean
=12. Substituting these values for
,
,
, and
into the formula
and calculating, we find the payment for the loan.
The monthly payment needed is $1,135.18.
-
The loan is for $28,500, which is the principal. The rate is 3.99%, so
= 0.0399. The term of the loan is 5 years, so
=5. Monthly payments means
= 12. Substituting these values for
,
,
, and
into the formula
and calculating, we find the payment for the loan.
In the following, calculate the payment necessary to pay off the loan with the given details. The payments are monthly.
A home improvement loan taken out for $17,950 at an annual interest rate of 7.5% for 10 years.
A solar panel installation loan taken out for $33,760 and an annual interest rate of 4.3% for 20 years.
Google Sheets has a formula to calculate the monthly payment necessary to pay off a loan with a specified interest rate and term. The formula is the PMT formula. It uses the principal , interest rate , and years. Follow these steps
Open a Google worksheet and click on any cell.
Type =-PMT(r/12,12*t,P).
Hit the enter key.
The cell displays the payment.
Please note the negative sign. Since Google Sheets is a spreadsheet program, is sees the payment as funds leaving the account, and so they are, by default, negative. The negative sign in front of the formula makes the result positive.
For example, for a $50,000 loan at 10.9% interest for 7 years, you would type =-PMT(0.109/12,12*7,50000). The formula and the result are shown in Figure 6.19.
Alternatively, you can also use an online calculator to find monthly payments for a loan, such as the one at Caluculator.net
Reading Amortization Tables
An amortization table or amortization schedule is a table that provides the details of the periodic payments for a loan where the payments are applied to both the principal and the interest. The principal of the loan is paid down over the life of the loan. Typically, the payments each period are equal. Importantly, one of the columns will show how much of each payment is used for interest, another column shows how much is applied to the outstanding principal, and another column shows the remaining principal or balance Figure 6.20.
Using the partial amortization table (Figure 6.23), answer the following questions.
Figure 6.- What is the loan amount (principal), the interest rate, and the term of the loan?
- How much is the monthly payment?
- How much remaining balance is there after the payment in month 15?
- How much was the interest in payment 10?
- What is the total of the interest paid after payment 18?
- What happens to the amount paid in interest each month?
- Answer
-
- Reading the values at the top of the table, we see the principal is $10,000, the interest rate is 4.75%, and has a term of 20 years.
- The monthly payment is listed below the term of the loan, and is $64.62.
- $9,613.83
- $38.68
- $697.01
- The amount paid to interest decreases each month.
Using the partial amortization table below, answer the following questions.
- What is the loan amount (principal), the interest rate, and the term of the loan?
- How much is the monthly payment?
- How much remaining balance is there after the payment in month 20?
- How much was the interest in payment 5?
- What is the total of the interest paid after payment 24?
- What happens to the amount paid to the principal each month?
Reading an Amortization Table
Cost of Finance
There are often costs associated with a loan beyond the interest being paid. The cost of finance of a loan is the sum of all costs, fees, interest, and other charges paid over the life of the loan.
Irena signed for a loan of $15,000 at 6.33% for 5 years. When she took out the loan, Irena paid a $750 origination fee. Over the course of the loan, she pays $2,537.96 in interest. What was her cost to finance the loan?
- Answer
-
The cost of finance is the sum is all interest and any fees paid for the loan. The fees paid were $750.00 and the interest was $2,537.96. Her cost of finance for this loan was $3,287.96.
Samantha takes out a $28,000 loan for 6 years at 5.5% interest. When she took out the loan, she paid $4,937.18 in interest, an origination fee of $1,400 and an application fee of $100. What was her cost of finance for this loan?
Check Your Understanding
Give three reasons for taking out a loan.
What is an installment loan?
In an installment loan what happens to the amount of the payment that is applied to interest in later payments compared to earlier payments?
An installment loan is paid monthly. The remaining principal is $5,498. If the interest rate is 12.9%, how much interest is paid that month?
A business loan is taken out for $250,000 for 15 years at 6.9% interest. What are the payments for the loan?
Consider the amortization table below. What is the balance after the eleventh payment?
The total interest paid on a loan is $38,519.50. The origination fee was $300 while the processing fee was $250. An additional fee was charged to the borrowers, amounting to another $475. How much was the cost of financing for this loan?


8.5.1: Memory Test
Lesson
Let's put it all together.
Exercise \(\PageIndex{1}\): Collecting a Sample
You teacher will give you a paper that lists a data set with 100 numbers in it. Explain whether each method of obtaining a sample of size 20 would produce a random sample.
Option 1: A spinner has 10 equal sections on it. Spin once to get the row number and again to get the column number for each member of your sample. Repeat this 20 times.
Option 2: Since the data looks random already, use the first two rows.
Option 3: Cut up the data and put them into a bag.
Option 4: Close your eyes and point to one of the numbers to use as your first value in your sample. Then, keep moving one square from where your finger is to get a path of 20 values for your sample.
Exercise \(\PageIndex{2}\): Sample Probabilities
Continue working with the data set your teacher gave you in the previous activity. The data marked with a star all came from students at Springfield Middle School.
- When you select the first value for your random sample, what is the probability that it will be a value that came from a student at Springfield Middle School?
- What proportion of your entire sample would you expect to be from Springfield Middle School?
- If you take a random sample of size 10, how many scores would you expect to be from Springfield Middle School?
- Select a random sample of size 10.
- Did your random sample have the expected number of scores from Springfield Middle School?
Exercise \(\PageIndex{3}\): Estimating a Measure of Center for the Population
- Decide which measure of center makes the most sense to use based on the distribution of your sample. Discuss your thinking with your partner. If you disagree, work to reach an agreement.
- Estimate this measure of center for your population based on your sample.
- Calculate the measure of variability for your sample that goes with the measure of center that you found.
Exercise \(\PageIndex{4}\): Comparing Populations
Using only the values you computed in the previous two activities, compare your sample to your partner's.
Is it reasonable to conclude that the measures of center for each of your populations are meaningfully different? Explain or show your reasoning.


11.6: Measures of Variation
Consider these three sets of quiz scores:
- Section A: 5 5 5 5 5 5 5 5 5 5
- Section B: 0 0 0 0 0 10 10 10 10 10
- Section C: 4 4 4 5 5 5 5 6 6 6
All three of these sets of data have a mean of 5 and median of 5, yet the sets of scores are clearly quite different. In section A, everyone had the same score; in section B half the class got no points and the other half got a perfect score, assuming this was a 10-point quiz. Section C was not as consistent as section A, but not as widely varied as section B.
In addition to the mean and median, which are measures of the "typical" or "middle" value, we also need a measure of how "spread out" or varied each data set is.
There are several ways to measure this "spread" of the data. The first is the simplest and is called the range .
The range is the difference between the maximum value and the minimum value of the data set.
Using the quiz scores from above,
For section A, the range is 0 since both maximum and minimum are 5 and \(5 – 5 = 0\)
For section B, the range is 10 since \(10 – 0 = 10\)
For section C, the range is 2 since \(6 – 4 = 2\)
In the last example, the range seems to be revealing how spread out the data is. However, suppose we add a fourth section, Section D, with scores 0 5 5 5 5 5 5 5 5 10.
This section also has a mean and median of 5. The range is 10, yet this data set is quite different than Section B. To better illuminate the differences, we’ll have to turn to more sophisticated measures of variation.
The standard deviation is a measure of variation based on measuring how far each data value deviates, or is different, from the mean. A few important characteristics:
- Standard deviation is always positive. Standard deviation will be zero if all the data values are equal, and will get larger as the data spreads out.
- Standard deviation has the same units as the original data.
- Standard deviation, like the mean, can be highly influenced by outliers.
Using the data from section D, we could compute for each data value the difference between the data value and the mean:
\(\begin{array}{|l|l|}
\hline \text { data value } & \text { deviation: data value - mean } \\
\hline 0 & 0-5=-5 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 5 & 5-5=0 \\
\hline 10 & 10-5=5 \\
\hline
\end{array}\)
We would like to get an idea of the "average" deviation from the mean, but if we find the average of the values in the second column the negative and positive values cancel each other out (this will always happen), so to prevent this we square every value in the second column:
We then add the squared deviations up to get \(25 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 25 = 50\). Ordinarily we would then divide by the number of scores, \(n\), (in this case, 10) to find the mean of the deviations. But we only do this if the data set represents a population; if the data set represents a sample (as it almost always does), we instead divide by \(n - 1\) (in this case, \(10 - 1 = 9\)).[1]
So in our example, we would have \(\frac{50}{10} = 5\) if section D represents a population and \(\frac{50}{9} =\) about 5.56 if section D represents a sample. These values (5 and 5.56) are called, respectively, the population variance and the sample variance for section D.
Variance can be a useful statistical concept, but note that the units of variance in this instance would be points-squared since we squared all of the deviations. What are points-squared? Good question. We would rather deal with the units we started with (points in this case), so to convert back we take the square root and get:
\[\text{population standard deviation} =\sqrt{\frac{50}{10}}=\sqrt{5} \approx 2.2 \nonumber \]
or
\[\text{sample standard deviation} =\sqrt{\frac{50}{9}} \approx 2.4 \nonumber \]
If we are unsure whether the data set is a sample or a population, we will usually assume it is a sample, and we will round answers to one more decimal place than the original data, as we have done above.
- Find the deviation of each data from the mean. In other words, subtract the mean from the data value.
- Square each deviation.
- Add the squared deviations.
- Divide by \(n\), the number of data values, if the data represents a whole population; divide by \(n – 1\) if the data is from a sample.
- Compute the square root of the result.
Computing the standard deviation for Section B above, we first calculate that the mean is 5. Using a table can help keep track of your computations for the standard deviation:
\(\begin{array}{|l|l|l|}
\hline \text { data value } & \text { deviation: data value - mean } & \text { deviation squared } \\
\hline 0 & 0-5=-5 & (-5)^{2}=25 \\
\hline 0 & 0-5=-5 & (-5)^{2}=25 \\
\hline 0 & 0-5=-5 & (-5)^{2}=25 \\
\hline 0 & 0-5=-5 & (-5)^{2}=25 \\
\hline 0 & 0-5=-5 & (-5)^{2}=25 \\
\hline 10 & 10-5=5 & (5)^{2}=25 \\
\hline 10 & 10-5=5 & (5)^{2}=25 \\
\hline 10 & 10-5=5 & (5)^{2}=25 \\
\hline 10 & 10-5=5 & (5)^{2}=25 \\
\hline 10 & 10-5=5 & (5)^{2}=25 \\
\hline
\end{array}\)
Assuming this data represents a population, we will add the squared deviations, divide by 10, the number of data values, and compute the square root:
\[\sqrt{\frac{25+25+25+25+25+25+25+25+25+25}{10}}=\sqrt{\frac{250}{10}}=5 \nonumber \]
Notice that the standard deviation of this data set is much larger than that of section D since the data in this set is more spread out.
For comparison, the standard deviations of all four sections are:
\(\begin{array}{|l|l|}
\hline \text { Section A: 5 5 5 5 5 5 5 5 5 5 } & \text { Standard deviation: 0 } \\
\hline \text { Section B: 0 0 0 0 0 10 10 10 10 10 } & \text { Standard deviation: 5 } \\
\hline \text { Section C: 4 4 4 5 5 5 5 6 6 6 } & \text { Standard deviation: 0.8 } \\
\hline \text { Section D: 0 5 5 5 5 5 5 5 5 10 } & \text { Standard deviation: 2.2 } \\
\hline
\end{array}\)
The price of a jar of peanut butter at 5 stores were: $3.29, $3.59, $3.79, $3.75, and $3.99. Find the standard deviation of the prices.
- Answer
-
Earlier we found the mean of the data was $3.682.
\(\begin{array}{|l|l|l|}
\hline \text { data value } & \text { deviation: data value - mean } & \text { deviation squared } \\
\hline 3.29 & 3.29-3.682=-0.391 & 0.153664 \\
\hline 3.59 & 3.59-3.682=-0.092 & 0.008464 \\
\hline 3.79 & 3.79-3.682=0.108 & 0.011664 \\
\hline 3.75 & 3.75-3.682=0.068 & 0.004624 \\
\hline 3.99 & 3.99-3.682=0.308 & 0.094864 \\
\hline
\end{array}\)This data is from a sample, so we will add the squared deviations, divide by 4, the number of data values minus 1, and compute the square root:
\(\sqrt{\frac{0.153664+0.008464+0.011664+0.004624+0.094864}{4}} \approx \$ 0.261\)
Where standard deviation is a measure of variation based on the mean, quartiles are based on the median.
Quartiles are values that divide the data in quarters.
The first quartile (\(Q_1\)) is the value so that 25% of the data values are below it; the third quartile (\(Q_3\)) is the value so that 75% of the data values are below it. You may have guessed that the second quartile is the same as the median, since the median is the value so that 50% of the data values are below it.
This divides the data into quarters; 25% of the data is between the minimum and \(Q_1\), 25% is between \(Q_1\) and the median, 25% is between the median and \(Q_3\), and 25% is between \(Q_3\) and the maximum value
While quartiles are not a 1-number summary of variation like standard deviation, the quartiles are used with the median, minimum, and maximum values to form a 5 number summary of the data.
The five number summary takes this form:
Minimum, \(Q_1\), Median, \(Q_3\), Maximum
To find the first quartile, we need to find the data value so that 25% of the data is below it. If \(n\) is the number of data values, we compute a locator by finding 25% of \(n\). If this locator is a decimal value, we round up, and find the data value in that position. If the locator is a whole number, we find the mean of the data value in that position and the next data value. This is identical to the process we used to find the median, except we use 25% of the data values rather than half the data values as the locator.
Begin by ordering the data from smallest to largest
Compute the locator: \(L = 0.25n\)
If \(L\) is a decimal value:
Round up to \(L+\)
Use the data value in the \(L+^{\text{th}}\) position
If \(L\) is a whole number:
Find the mean of the data values in the \(L^{\text{th}}\) and \(L+1^{\text{th}}\) positions.
Use the same procedure as for \(Q_1\), but with locator: \(L = 0.75n\)
Examples should help make this clearer.
Suppose we have measured 9 females and their heights (in inches), sorted from smallest to largest are:
59 60 62 64 66 67 69 70 72
To find the first quartile we first compute the locator: 25% of 9 is \(L = 0.25(9) = 2.25\). Since this value is not a whole number, we round up to 3. The first quartile will be the third data value: 62 inches.
To find the third quartile, we again compute the locator: 75% of 9 is \(0.75(9) = 6.75\). Since this value is not a whole number, we round up to 7. The third quartile will be the seventh data value: 69 inches.
Suppose we had measured 8 females and their heights (in inches), sorted from smallest to largest are:
59 60 62 64 66 67 69 70
To find the first quartile we first compute the locator: 25% of 8 is \(L = 0.25(8) = 2\). Since this value is a whole number, we will find the mean of the 2 nd and 3 rd data values: (60+62)/2 = 61, so the first quartile is 61 inches.
The third quartile is computed similarly, using 75% instead of 25%. \(L = 0.75(8) = 6\). This is a whole number, so we will find the mean of the 6 th and 7 th data values: \(\frac{67+69}{2} = 68\), so \(Q_3\) is 68.
Note that the median could be computed the same way, using 50%.
The 5-number summary combines the first and third quartile with the minimum, median, and maximum values.
For the 9 female sample, the median is 66, the minimum is 59, and the maximum is 72. The 5 number summary is: 59, 62, 66, 69, 72.
For the 8 female sample, the median is 65, the minimum is 59, and the maximum is 70, so the 5 number summary would be: 59, 61, 65, 68, 70.
Returning to our quiz score data. In each case, the first quartile locator is \(0.25(10) = 2.5\), so the first quartile will be the 3 rd data value, and the third quartile will be the 8 th data value. Creating the five-number summaries:
\(\begin{array}{|l|l|}
\hline \text { Section and data } & \text { 5-number summary } \\
\hline \text { Section A: 5 5 5 5 5 5 5 5 5 5 } & 5,5,5,5,5 \\
\hline \text { Section B: 0 0 0 0 0 10 10 10 10 10 } & 0,0,5,10,10 \\
\hline \text { Section C: 4 4 4 5 5 5 5 6 6 6 } & 4,4,5,6,6 \\
\hline \text { Section D: 0 5 5 5 5 5 5 5 5 10 } & 0,5,5,5,10 \\
\hline
\end{array}\)
Of course, with a relatively small data set, finding a five-number summary is a bit silly, since the summary contains almost as many values as the original data.
The total cost of textbooks for the term was collected from 36 students. Find the 5 number summary of this data.
$140 $160 $160 $165 $180 $220 $235 $240 $250 $260 $280 $285
$285 $285 $290 $300 $300 $305 $310 $310 $315 $315 $320 $320
$330 $340 $345 $350 $355 $360 $360 $380 $395 $420 $460 $460
- Answer
-
The data is already in order, so we don’t need to sort it first.
The minimum value is $140 and the maximum is $460.
There are 36 data values so \(n=36 . n / 2=18,\) which is a whole number, so the median is the mean of the \(18^{\text {th }}\) and \(19^{\text {th }}\) data values, \(\$ 305\) and \(\$ 310\). The median is \(\$ 307.50\)
To find the first quartile, we calculate the locator, \(L=0.25(36)=9 .\) since this is a whole number, we know \(\mathrm{Q}_{1}\) is the mean of the \(9^{\text {th }}\) and \(10^{\text {th }}\) data values, \(\$ 250\) and \(\$ 260 . \mathrm{Q}_{1}=\) \(\$ 255\)
To find the third quartile, we calculate the locator, \(L=0.75(36)=27 .\) since this is a whole number, we know \(Q_{3}\) is the mean of the \(27^{\text {th }}\) and \(28^{\text {th }}\) data values, \(\$ 345\) and \(\$ 350\).
\(\mathrm{Q}_{3}=\$ 347.50\)The 5 number summary of this data is: $140, $255, $307.50, $347.50, $460
Returning to the household income data from earlier, create the five-number summary.
\(\begin{array}{|l|l|}
\hline \textbf { Income (thousands of dollars) } & \textbf { Frequency } \\
\hline 15 & 6 \\
\hline 20 & 8 \\
\hline 25 & 11 \\
\hline 30 & 17 \\
\hline 35 & 19 \\
\hline 40 & 20 \\
\hline 45 & 12 \\
\hline 50 & 7 \\
\hline
\end{array}\)
Solution
By adding the frequencies, we can see there are 100 data values represented in the table. In Example 20, we found the median was $35 thousand. We can see in the table that the minimum income is $15 thousand, and the maximum is $50 thousand.
To find \(Q_1\), we calculate the locator: L = 0.25(100) = 25. This is a whole number, so \(Q_1\) will be the mean of the 25 th and 26 th data values.
Counting up in the data as we did before,
\(\begin{array}{ll} \text{There are 6 data values of \$15, so} & \text{Values 1 to 6 are \$15 thousand} \\ \text{The next 8 data values are \$20, so} & \text{Values 7 to (6+8)=14 are \$20 thousand} \\ \text{The next 11 data values are \$25, so} & \text{Values 15 to (14+11)=25 are \$25 thousand} \\ \text{The next 17 data values are \$30, so} & \text{Values 26 to (25+17)=42 are \$30 thousand} \end{array}\)
The 25 th data value is $25 thousand, and the 26 th data value is $30 thousand, so \(Q_1\) will be the mean of these: \((25 + 30)/2 = \$27.5\) thousand.
To find \(Q_3\), we calculate the locator: \(L = 0.75(100) = 75\). This is a whole number, so \(Q_3\) will be the mean of the 75 th and 76 th data values. Continuing our counting from earlier,
\(\begin{array}{ll} \text{The next 19 data values are $35, so} & \text{Values 43 to (42+19)=61 are \$35 thousand} \\ \text{The next 20 data values are \$40, so} & \text{Values 61 to (61+20)=81 are \$40 thousand} \end{array}\)
Both the 75 th and 76 th data values lie in this group, so \(Q_3\) will be $40 thousand.
Putting these values together into a five-number summary, we get: 15, 27.5, 35, 40, 50
Note that the 5 number summary divides the data into four intervals, each of which will contain about 25% of the data. In the previous example, that means about 25% of households have income between $40 thousand and $50 thousand.
For visualizing data, there is a graphical representation of a 5-number summary called a box plot , or box and whisker graph.
A box plot is a graphical representation of a five-number summary.
To create a box plot, a number line is first drawn. A box is drawn from the first quartile to the third quartile, and a line is drawn through the box at the median. “Whiskers” are extended out to the minimum and maximum values.
The box plot below is based on the 9 female height data with 5 number summary:
59, 62, 66, 69, 72.
The box plot below is based on the household income data with 5 number summary:
15, 27.5, 35, 40, 50
Create a boxplot based on the textbook price data from the last Try it Now.
- Answer
-
Box plots are particularly useful for comparing data from two populations.
The box plot of service times for two fast-food restaurants is shown below.
While store 2 had a slightly shorter median service time (2.1 minutes vs. 2.3 minutes), store 2 is less consistent, with a wider spread of the data.
At store 1, 75% of customers were served within 2.9 minutes, while at store 2, 75% of customers were served within 5.7 minutes.
Which store should you go to in a hurry? That depends upon your opinions about luck – 25% of customers at store 2 had to wait between 5.7 and 9.6 minutes.
The boxplot below is based on the birth weights of infants with severe idiopathic respiratory distress syndrome (SIRDS)[2]. The boxplot is separated to show the birth weights of infants who survived and those that did not.
Comparing the two groups, the boxplot reveals that the birth weights of the infants that died appear to be, overall, smaller than the weights of infants that survived. In fact, we can see that the median birth weight of infants that survived is the same as the third quartile of the infants that died.
Similarly, we can see that the first quartile of the survivors is larger than the median weight of those that died, meaning that over 75% of the survivors had a birth weight larger than the median birth weight of those that died.
Looking at the maximum value for those that died and the third quartile of the survivors, we can see that over 25% of the survivors had birth weights higher than the heaviest infant that died.
The box plot gives us a quick, albeit informal, way to determine that birth weight is quite likely linked to survival of infants with SIRDS.
[1] The reason we do this is highly technical, but we can see how it might be useful by considering the case of a small sample from a population that contains an outlier, which would increase the average deviation: the outlier very likely won't be included in the sample, so the mean deviation of the sample would underestimate the mean deviation of the population; thus we divide by a slightly smaller number to get a slightly bigger average deviation.
[2] van Vliet, P.K. and Gupta, J.M. (1973) Sodium bicarbonate in idiopathic respiratory distress syndrome. Arch. Disease in Childhood , 48 , 249–255. As quoted on http://openlearn.open.ac.uk/mod/ouco...§ion=1.1.3


3.3: Andrew Marvell (1621-1678)
Andrew Marvell’s father, the Reverend Andrew Marvell, died from drowning after a boating accident, thereby possibly curtailing Marvell’s academic career and possibly leading to his taking religious orders. Marvell probably studied at the Hull Grammar School; at the age of twelve, he entered Trinity College, Cambridge, where he earned his B.A. in four years, then began studying for a Master of Art (which he did not complete).
He may have traveled the Continent during the Civil War. He secured a position as tutor to the daughter of Lord Thomas Fairfax (1612-1671), a Parliamentarian general. Marvell’s Parliamentarian sympathies may have won him his subsequent positions, as tutor to William Dutton, the ward of Oliver Cromwell; as Latin Secretary, assisting John Milton in translations and diplomatic correspondence; and as Minister of Parliament, a position Marvell held until his death but that began before the Restoration. As a politician, Marvell seems to have promoted the interests of religious and political dissenters, though he did not actively oppose the Restoration. He may have saved Milton’s life after the Restoration, a time of reprisal when many “rebels” were executed. His poem “On Mr. Milton’s Paradise Lost ,” praises Milton’s genius at a time when Milton was exiled for his political activities.
Scholars have sometimes divided Marvell’s work into pre- and post-Restoration, with most of his poetry being placed pre- and most of his prose, particularly his political writing, being placed post-Restoration. All of his writing is characterized by its intellect, wit, and often abstruse logic. John Dryden noted Marvell’s tendency towards the abstract, especially when dealing with emotional subjects. In the twentieth century, T. S. Eliot (1888-1965) linked Marvell with the metaphysical poets in their uniting reason and emotion. Like that of other metaphysical poets, such as John Donne’s, Marvell’s poetry uses puns, paradoxes, and incongruous images. What seems unique to Marvell is his willingness to maintain ambiguity, to give all sides of a subject their due, to complicate rather than simplify. In “To His Coy Mistress,” he can adore his mistress’s eyes, forehead, and “the rest” (16) yet still roll all her sweetness and strength into “one ball” (42).
3.8.1: “A Dialogue, Between The Resolved Soul, and Created Pleasure”
(1681)
Courage my Soul, now learn to wield
The weight of thine immortal Shield.
Close on thy Head thy Helmet bright.
Ballance thy Sword against the Fight.
See where an Army, strong as fair,
With silken Banners spreads the air.
Now, if thou bee’st that thing Divine,
In this day’s Combat let it shine:
And shew that Nature wants an Art
To conquer one resolved Heart.
Pleasure.
Welcome the Creations Guest,
Lord of Earth, and Heavens Heir.
Lay aside that Warlike Crest,
And of Nature’s banquet share:
Where the Souls of fruits and flow’rs
Stand prepar’d to heighten yours.
Soul.
I sup above, and cannot stay
To bait so long upon the way.
Pleasure.
On these downy Pillows lye,
Whose soft Plumes will thither fly:
On these Roses strow’d so plain
Lest one Leaf thy Side should strain.
Soul.
My gentler Rest is on a Thought,
Conscious of doing what I ought.
Pleasure.
If thou bee’st with Perfumes pleas’d,
Such as oft the Gods appeas’d,
Thou in fragrant Clouds shalt show
Like another God below.
Soul.
A Soul that knowes not to presume
Is Heaven’s and its own perfume.
Pleasure.
Every thing does seem to vie
Which should first attract thine Eye:
But since none deserves that grace,
In this Crystal view thy face.
Soul.
When the Creator’s skill is priz’d,
The rest is all but Earth disguis’d.
Pleasure.
Heark how Musick then prepares
For thy Stay these charming Aires;
Which the posting Winds recall,
And suspend the Rivers Fall.
Soul.
Had I but any time to lose,
On this I would it all dispose.
Cease Tempter. None can chain a mind
Whom this sweet Chordage cannot bind.
Chorus.
Earth cannot shew so brave a Sight
As when a single Soul does fence
The Batteries of alluring Sense,
And Heaven views it with delight.
Then persevere: for still new Charges sound:
And if thou overcom’st thou shalt be crown’d.
Pleasure.
All this fair, and cost, and sweet,
Which scatteringly doth shine,
Shall within one Beauty meet,
And she be only thine.
Soul.
If things of Sight such Heavens be,
What Heavens are those we cannot see?
Pleasure.
Where so e’re thy Foot shall go
The minted Gold shall lie;
Till thou purchase all below,
And want new Worlds to buy.
Soul.
Wer’t not a price who’ld value Gold?
And that’s worth nought that can be sold.
Pleasure.
Wilt thou all the Glory have
That War or Peace commend?
Half the World shall be thy Slave
The other half thy Friend.
Soul.
What Friends, if to my self untrue?
What Slaves, unless I captive you?
Pleasure.
Thou shalt know each hidden Cause;
And see the future Time:
Try what depth the Centre draws;
And then to Heaven climb.
Soul.
None thither mounts by the degree
Of Knowledge, but Humility.
Chorus.
Triumph, triumph, victorious Soul;
The World has not one Pleasure more:
The rest does lie beyond the Pole,
And is thine everlasting Store.
3.8.2 “On a Drop of Dew”
(1681)
See how the Orient Dew,
Shed from the Bosom of the Morn
Into the blowing Roses,
Yet careless of its Mansion new;
For the clear Region where ’twas born
Round in its self incloses:
And in its little Globes Extent,
Frames as it can its native Element.
How it the purple flow’r does slight,
Scarce touching where it lyes,
But gazing back upon the Skies,
Shines with a mournful Light;
Like its own Tear,
Because so long divided from the Sphear.
Restless it roules and unsecure,
Trembling lest it grow impure:
Till the warm Sun pitty it’s Pain,
And to the Skies exhale it back again.
So the Soul, that Drop, that Ray
Of the clear Fountain of Eternal Day,
Could it within the humane flow’r be seen,
Remembring still its former height,
Shuns the sweat leaves and blossoms green;
And, recollecting its own Light,
Does, in its pure and circling thoughts, express
The greater Heaven in an Heaven less.
In how coy a Figure wound,
Every way it turns away:
So the World excluding round,
Yet receiving in the Day.
Dark beneath, but bright above:
Here disdaining, there in Love.
How loose and easie hence to go:
How girt and ready to ascend.
Moving but on a point below,
It all about does upwards bend.
Such did the Manna’s sacred Dew destil;
White, and intire, though congeal’d and chill.
Congeal’d on Earth: but does, dissolving, run
Into the Glories of th’ Almighty Sun.
3.8.3: “The Coronet”
(1681)
When for the Thorns with which I long, too
With many a piercing wound, (long,
My Saviours head have crown’d,
I seek with Garlands to redress that Wrong:
Through every Garden, every Mead,
I gather flow’rs (my fruits are only flow’rs)
Dismantling all the fragrant Towers
That once adorn’d my Shepherdesses head.
And now when I have summ’d up all my store,
Thinking (so I my self deceive)
So rich a Chaplet thence to weave
As never yet the king of Glory wore:
Alas I find the Serpent old
That, twining in his speckled breast,
About the flow’rs disguis’d does fold,
With wreaths of Fame and Interest.
Ah, foolish Man, that would’st debase with them,
And mortal Glory, Heavens Diadem!
But thou who only could’st the Serpent tame,
Either his slipp’ry knots at once untie,
And disintangle all his winding Snare:
Or shatter too with him my curious frame:
And let these wither, so that he may die,
Though set with Skill and chosen out with Care.
That they, while Thou on both their Spoils dost tread,
May crown thy Feet, that could not crown thy Head.
3.8.4: “To his Coy Mistress”
(1681)
Had we but World enough, and Time,
This coyness Lady were no crime.
We would sit down, and think which way
To walk, and pass our long Loves Day.
Thou by the Indian Ganges side
Should’st Rubies find: I by the Tide
Of Humber would complain. I would
Love you ten years before the Flood:
And you should if you please refuse
Till the Conversion of the Jews.
My vegetable Love should grow
Vaster then Empires, and more slow.
An hundred years should go to praise
Thine Eyes, and on thy Forehead Gaze.
Two hundred to adore each Breast:
But thirty thousand to the rest.
An Age at least to every part,
And the last Age should show your Heart.
For Lady you deserve this State;
Nor would I love at lower rate.
But at my back I alwaies hear
Times winged Charriot hurrying near:
And yonder all before us lye
Desarts of vast Eternity.
Thy Beauty shall no more be found;
Nor, in thy marble Vault, shall sound
My ecchoing Song: then Worms shall try
That long preserv’d Virginity:
And your quaint Honour turn to durst:
And into ashes all my Lust.
The Grave’s a fine and private place,
But none I think do there embrace.

Let us roll all our Strength, and all
Our sweetness, up into one Ball
And tear our Pleasures with rough strife,
Thorough the Iron gates of Life.
Thus, though we cannot make our Sun
Stand still, yet we will make him run.