4.6: Structures and Sculptures (1800-1900)
Introduction
With the Industrial Revolution came the ability for mass production of goods and materials, extensive manufacturing facilities, an abundance of coal and power, transportation systems, and the accumulation of money by a few. Steel was a vital part of the revolution, the main component in buildings, railroads, and shipping. Gustave Eiffel was able to have steel manufactured to support his tower because of steam power to mine the raw materials and run the manufacturing plants. William Morris designed patterns for textiles based on new methods of dyeing, weaving, and manufacturing materials. Sculptors no longer relied on money from the government or religious sources; private citizens also supported the arts.
Gustave Eiffel
Gustave Eiffel (1832-1923) was a French engineer who designed bridges and viaducts for different projects in France. He graduated from one of France's prestigious engineering schools, then worked as a researcher in a company where he created a new method of supporting the railroad's bridges. He was also hired to design girders for a new gallery, studying cast iron properties and applying his theories to casting. His reputation grew, and he became one of the leading engineers in France, employing his innovative engineering theories to bridges and buildings. To support the new proposed exposition in France, engineers designed a preliminary concept for a tower. Eiffel endorsed the plan and then acquired the patents and rights to the design.
After a commission for the tower selected Eiffel's design, he started working on the tower (4.6.1), and the critics began to object. Some of the important artists sent a letter stating:
…To bring our arguments home, imagine for a moment a giddy, ridiculous tower dominating Paris like a gigantic black smokestack, crushing under its barbaric bulk Notre Dame, the Tour Saint-Jacques, the Louvre, the Dome of Les Invalides, the Arc de Triomphe; all of our humiliated monuments will disappear in this ghastly dream. And for twenty years…we shall see stretching like a blot of ink the hateful shadow of the hateful column of bolted sheet metal. [1]
Eiffel responded with a discussion about the pyramids and their grandeur on the aesthetic impact of architectural structures. He argued his tower would be the highest thing ever built and look as beautiful in Paris as the pyramids did in Egypt. Eiffel built the tower during the time of the industrial revolution when inventions were creating new societies, trade grew, and lives were altered under increasing prosperity. Many believed Eiffel's tower was the crown.
The engineers drew over 5,000 drawings for the tower, more than 100 workers made the parts, and another 130 assembled the 18.000 pieces at the site. The foundations had to be dug by hand for the four legs of the tower. The completed tower used over 7,000 tons of iron in its design to account for the resistance to wind forces. He believed metal's resistance to the movement was superior to wood or stone. When the second level was completed in May 1888 (4.6.2), Eiffel took officials to the level, amazing them with the view. When it was completed, the tower was the highest structure in the world until 1930, and the Chrysler Building in the United States was built.
Auguste Rodin
Auguste Rodin (1840-1917), whose parents were ordinary working people in Paris, trained early in art and anatomical structures and then worked as a sculpture apprentice. When he went to Italy, he studied the work of Michelangelo, a work that influenced how Rodin created his sculptures. Rodin's work did not follow the traditional decorative or mythological ideas of sculpture; instead, they were realistic and complex, posed in emotional positions. He positioned multiple models in his studios, forming quick clay models that he used later to make plaster casts and then bronze or marble statues. As time passed, he did not follow traditional positions for the body or attachments for parts of the statue; the surfaces were rough, often pock-marked. Some historians believe he is the most significant sculptor of modern times.
The Gates of Hell (4.6.3) was his first government commission. He sketched multiple ideas, even making clay models, all based on the Divine Comedy by Dante. When it was time to deliver the giant 6.4 meters high doors, Rodin was not finished with them. He made clay models for each of the different figures on the gates, which continually dried before he was finished, and finally removed each one, making plaster casts to preserve each figure. This also allowed him to remake, enlarge or move each of the figures, some of them only 15 centimeters tall and ranging up to one meter high. The plaster casts of each statue became the basis for individual sculptures and appeared on the gates. The final gates were not cast for over thirty years, and were never cast in bronze during Rodin's life, only cast later after his death.
The Thinker (4.6.4) was part of the Gates of Hell , not originally a standalone sculpture. As part of the gate's panel, he sits at the top of the lintel on the door, gazing down. Rodin talked about the statue as a poet, an image of a creative person, and the agonizing over his world. Rodin described him as "What makes my Thinker think is that he thinks not only with his brain, with his knitted brow, his distended nostrils, and compressed lips, but with every muscle of his arms, back, and legs, with his clenched fist and gripping toes." [2] The Thinker has been cast multiple times from Rodin's original clay sculpture along with newer castings, not part of the original image.
The French government wanted public monuments to honor French patriots of the past and commissioned Rodin to build the tribute. One theme the government chose was based on six wealthy men from Calais who volunteered as hostages to one of the English kings to stop the siege on the town. The government asked Rodin to make a statue of the group leader; however, he made a model of all six of the men, an image the government accepted, The Burghers of Calais (4.6.5). Rodin worked on each person individually, not following traditional heroic settings or images on a pedestal with other allegorical images. Instead, the men portrayed their agony and pain in the situation. They were all installed on the top of a pedestal instead of standing individually as Rodin wanted. Twelve castings of the sculpture have been made, including the one at Stanford University (4.6.6), where the men each stand alone as Rodin originally intended.
Camille Claudel
Camille Claudel (1863-1943) was from northern France and was recognized at an early age for her artistic talent and beauty. She studied sculpture at an academy and had her studio until Rodin asked her to be his assistant. One advantage this opportunity gave her was the ability to study the nude figure and its anatomy; a subject women could not study at the time. During her time in Rodin's studio, she helped model some of his sculptures while developing her career.
Her relationship with Rodin was stormy, an affair lasting ten years, hard work and harsh clashes, and Rodin returned to another woman he married. She finally left to work on her own. Others criticized her work and the press, partly based on her assumed position with Rodin as not only a teacher but her lover. As she was working, Claudel developed symptoms of delirium and dementia, and she was committed to an asylum, stopped working, staying there for thirty years until her death. Vertumnus and Pomona (4.6.7) was based on an old play from India about a woman's reunion with her husband when the magic spell was removed. Claudel tried to obtain a commission from the state and was refused; however, a private citizen commissioned the work, carved in white marble and standing on a base of red marble.
The Age of Maturity (4.6.8) originally was a commission by the French government that was canceled after the plaster version was created and before a bronze could be cast. Later two bronze statues were cast, and the plaster was destroyed. The sculpture has three figures, an older man who is in the embrace of an older woman as the kneeling younger woman reaches out. Many view this as a statement of life, youth aging into maturity, and finally death, while others interpret the statue as Rodin abandoning Claudel as he returns to another lover. Rodin did not like the work, and some think he influenced the commissioner to reject the sculpture.
Daniel Chester French
Daniel Chester French (1850-1931) is one of America's leading monuments sculptors. Born and raised in the New England area, he studied art and sculpture, earning a few commissions for public art. In his late twenties, the French went to Italy to study, not following the path others took to study in Paris. He returned to America, created several commissions, and then went to Paris for a year to study the French methods.
When he returned, one of his major commissions was the bronze memorial statue for Dr. Gallaudet, who founded the school for the deaf in Washington D.C. The sculpture (4.6.9) portrays Dr. Gallaudet seated next to the student Alice Cogswell. He uses sign language to spell the letter 'a' to the girl who copies him, representing a new method of education for those who are hearing.
French seldom sketched his ideas, preferring to create clay models. He was commissioned to make the statue for a new memorial to honor Abraham Lincoln (4.6.10). The base and columns made to enclose the statue were designed by Henry Bacon, whom the French worked with closely. The original size for the statute of Lincoln was planned to be 3 meters high; the size French made for the clay model. When it was taken to the site, he knew the size would not work and reworked the plan, a 5.8-meter-tall Lincoln, one of the most iconic statues in the world. French made the final sculpture from 28 blocks of marble; his chisel marks are still visible in some places. Lincoln sits, gazing straight ahead, a solemn look on his face as his expressive hands rest on the chair, the American flag draped over the back of the chair.
Harriet Hosmer
Harriet Hosmer (1830-1908) was one of the first American women to become a professional sculptor and was thought of as the eminent female sculptor of the period, paving the way for other women sculptors. As a child, her mother and three siblings died from tuberculosis, and because she was considered feeble, her father encouraged her to try different sports to build her strength. She became an expert in riding, rowing, swimming, and skating. She was skilled in working with clay, modeling figures, and studying anatomy with her father, a physician. Her first attempt at sculpting was successful; she went to Rome to study, knowing America did not have any schools where women could work with marble or use live nude models.
In Rome, she lived and worked in a colony of different writers and artists, including several American female sculptors who worked with marble. The writer Henry James called them "a strange sisterhood of lady sculptors'" and "the white marmorean flock," [3] and Hosmer was considered their leader. She had a series of relationships with other women and ended with a commitment to Lady Louisa Ashburton for twenty-five years. When Hosmer returned to America later in life, Hosmer became an activist in the women's rights movement and a friend of Susan B. Anthony. In Hosmer's later years, she spent time on different inventions and had a patent on the process she believed changed limestone into marble.
The majority of her work was based on tragic women from history, mythology, or literature. Zenobia in Chains (4.6.11) was one of her early works and financial success for Hosmer. The sculpture depicts the queen in the third century who was captured by the Romans, wrapped in chains, and paraded through the streets. Her clothing is layered in exquisite folds, and the details of the chain demonstrate Hosmer's ability to work with the complexity of marble. At the time, some critics did not believe a woman could create the complex, detailed statue standing 213.36 centimeters high. They thought she would not have enough power in her arms and hands to carve the marble.
The Sleeping Faun (4.6.12) depicts a woodland spirit inspired by the mythological forms from ancient Rome. Hosmer had a unique sense of humor reflected in the mischievous smile on the half-goat and half-human satyr who tied the faun's clothing to the tree stump, the perfect image of Hosmer's mastery of the neoclassical style. One critic stated, "If it had been discovered among the ruins of Rome or Pompeii, it would have been pronounced one of the best Grecian statues." [4]
When Hosmer was in Rome, she met the well-known poets from England, Robert and Elizabeth Barrett Browning. Hosmer asked if she could model their hands, and they agreed. She kept the hands (4.6.13) exactly are they were formed in the mold to maintain the textural characteristics of the work. Each person's hand is identifiable by the size of their hand and the cuffs of their shirts as it appears on the wrists. The hands were initially made in marble as a present for her niece.
Edmonia Lewis
Edmonia Lewis (1844-1907), the first woman of her heritage to become an internationally known sculptor, was born in New York, the daughter of a free African-American father and her mother from the Native American Anishinaabe. Her parents died when she was nine, and she lived with different relatives, frequently helping her aunt weave Ojibwe baskets to sell to tourists. Her older brother paid for her tuition in high school, a place she left after three years stating, "Until I was twelve years old I led this wandering life, fishing, and swimming…and making moccasins. I was then sent to school for three years in [McGrawville] but was declared to be wild--they could do nothing with me." [5] Abolitionists sent her to Oberlin College to study art, one of the few universities to admit women or people of differing ethnicities. However, she encountered multiple problems during this period, finally leaving a semester before graduating.
Lewis went to Boston in 1864 to pursue her dream of becoming a sculptor. With the help of the abolitionists, she worked with another artist before opening her studio, successfully making statues. Lewis went to Rome to further her career with her success in hand, staying there for much of her life. She expanded her neoclassical style to include themes from her heritage. Lewis was part of the sisterhood of lady sculptors, joining the other female sculptors in Rome.
Lewis frequently was inspired by her Native American and African American background to define the subject matter of her work. Based on Henry Wadsworth Longfellow's poem, The Song of Hiawatha, she honed several marble sculptures of Hiawatha (4.6.14) and Minnehaha (4.6.15). The two cabinet-sized busts wore romanticized Native American dress, characterizing the two ill-fated lovers. The Hiawatha in Wadsworth's poem was considered to be Anishnaabe (Chippewa), the same tribe as Lewis' ancestors.
Lewis depicted Cleopatra (4.6.16) at the time of her death from the poisonous snake's bite. Cleopatra is dressed in regal clothing, dying as she sat on her throne. The sphinx heads on each side of the throne symbolize her two twins. Most sculptors portray Cleopatra shortly before death, while Lewis decided to present Cleopatra after death, a concept criticized as shocking and repulsive. When the statue was first shown in America, she got rave reviews. Shortly after the statue's debut, it was presumed lost until a century later, appeared "at a Chicago saloon, marking a horse's grave at a suburban racetrack, and eventually reappearing at a salvage yard in the 1980s." [6]
Anne Whitney
Anne Whitney (1821-1915) was born in Massachusetts to a family of abolitionists who fought against slavery and for women's rights. She was a writer and then studied sculpture, opening her studio. When Whitney was only twenty-five, Whitney started a school for girls in Massachusetts. She moved to Rome after the civil war, studying both bronze and marble and using nude models who were male. She also was considered part of the sisterhood of women, associating with Edmonia Lewis, Harriet Hosmer, and others before she returned to America.
Early in her career, Whitney and all women were limited in what they studied, unable to take classes in life drawing or see plaster casts of humans in a coed classroom. If women wanted to visit an art gallery, any forms of nude men had their genitalia covered. So, she began making busts, the shoulders and head a safe form for female artists to pursue. A local shipowner commissioned her to make a sculpture of his daughter, Laura Brown (4.6.17), who was two or three at the time. The innocence of the young girl is evident in her half-smile and slightly plump body. Whitney is quoted as saying, "The likeness is good and the modeling I think the best by far I have done. It has been a great labor. The perpetually ranging curves of a child's face, the impossibility of getting a half moment's fixed look, and this child's expression being the most mobile…I ever saw, made altogether the work for some time almost a despair." [7]
On one of her journeys to Italy, she studied French sculpture procedures, using the methods to create her bust of Le Modele (4.6.18), based on concepts of Realism. She fashioned the image of a peasant woman, exaggerating the character of her wrinkles. The statue was cast in bronze, the in-depth details reflecting shadows and light.
Charles Sumner
A Harvard graduate, Charles Sumner (4.6.19) was a fervent abolitionist who became a senator from Massachusetts and worked on the legislation to abolish slavery. After he died, the city of Boston wanted to erect a statue in his honor, asking for artists to apply for the commission. Whitney had devoted herself to social justice and designed a memorial sculpture of Charles Sumner for the contest. The selected winner portrayed Sumner sitting on a seat, holding a book in his hand while attentively looking out over the area. The committee thought it represented the thoughtfulness and spirit of Sumner and Whitney won the national contest. However, someone told the committee a scandalous fact: a woman proposed the statue, and the committee selected the second-place design. "She was denied the commission after the judges discovered she was a woman. No woman, said the learned gentlemen, should attempt to model a man's legs: it was indelicate, and furthermore, it would never be successful." [8] The plaster model she made was stored away for over thirty years until 1902, when an anonymous donor had the bronze version of the statue cast and moved to the gate at Harvard.
William Morris
William Morris (1834-1896) was an artist and designer who changed the styles and fashions of the era. Coming from a wealthy family, he was educated privately and continued to Oxford. Morris founded a firm with friends, a successful company specializing in wallpaper, fabric, some furniture, even stained-glass windows, and changing interior decoration designs. Morris was also a social activist who led him to start a publishing company, writing and illustrating many of their books.
Morris aspired to construct a home in a rural area near London, surrounded by orchards, hills, and streams. He worked with Philip Webb as a co-designer for the house with Medieval and Gothic influences, designing an early version of the Arts and Crafts style. The Red House (4.6.20) was two stories high, made of brick with red tiles on the pitched roof some say resembled witches' hats. The different windows were defined separately in multiple styles for each room instead of reflecting an exterior symmetry. The house was severe in design and furnishings, unlike the excessive Victorian ornamentation of most buildings. Morris designed everything for the interior: fixed furniture, drapery, wall coverings, tableware, and even candlesticks. When Morris and his family lived there, he recognized the problems with the house; the north-facing was exceptionally cold in winter, the isolation made it hard for physicians to visit Morris, who had health problems, and the commute to the railway station was long. He sold the house after living there for only five years. Currently, the house has been restored and is part of the National Trust system in England.
Morris wanted his designs to be historically based and studied historical methods of dyeing and printing. He also based multiple designs on the hedgerows and gardens that grew in England. He designed over fifty types of wallpapers, designed as a radical departure from the Victorian styles of the day. Snakeshead (4.6.21) is printed on cotton, showing the balance and subtle formation of the natural form. During his studies, he learned the techniques used in India and how they strongly contrasted the colors and converted three-dimensional designs to flat patterns. He also changed the way dyes were used, moving from the chemical dyes to organic ingredients, for example, using walnut shells to make a brown color. Because the designs were complex, the fabric had to be double woven to achieve deep, intricate colors.
One of Morris's first tile designs (4.6.22) was for his Red House, leading him to add ceramics and tile to his business line of products. He used the same ideas on the tile as he did for fabric, well-formed and symmetrical designs.
Morris was also a writer; most of his early work was based on his political views. He wanted to reform how books were made and bring artistry to the printed page, so he started his own publishing company. Morris wrote a book based on his imagination, The Well at the World's End (4.6.23), one of the first books considered fantasy fiction, not just about dreams or travels around the world, but another invented world. He had his partner do the illustration, and Morris designed the complicated border using grapes, vines, leaves, and a large typeface.
Charles Edenshaw
Charles Edenshaw (1839-1920) was born in the Skidegate, a Haida village in British Columbia, Canada. His lineage was from the Haida matrilineal organization, and his birth name: Da.a xiignag. He was known for carving wood and argillite, a rock similar to shale; fractured, veined and generally deformed. However, it does not foliate like shale. Edenshaw was considered a master of the formline design system; the U, S, and ovoid forms were used as outlines and design elements in Northwestern indigenous art. Form lines change thickness when they flow around corners, and interconnected form lines create the design. The form lines are two-dimensional on flat surfaces and three-dimensional on totem poles or masks. [9] "Edenshaw's name has become synonymous with classic Northwest Coast style, and his work has inspired nearly every serious artist in the region." [10]
In the 1850s, the indigenous populations in the Pacific Northwest were devastated by smallpox. The Canadian government outlawed the ceremonial raising of immense totem poles, leaving the native people unable to continue traditions, including making totem poles. Edenshaw started carving model totem poles, carrying on the tradition in a smaller format, bringing the imagery and artistic conventions to life and maintaining their cultural identity and oral history for the next generation. He used argillite to carve the model totem poles (4.6.24, 4.6.25), a significant volume of his work. By the end of the 1800s, Edenshaw's model totem poles became the characteristic example of argillite carving.
The industrial revolution changed Europe and America with mass production of products and new types of materials available. Expanded populations had more money; towns and private citizens could afford to purchase art creating a marketplace for artists. During this period, female artists started to realize their potential and their right to have an identifiable career in art. All three sculptors in this section used bronze to produce the finished art sculptures and the original cast could be used over and over to create the same piece of art. Producing multiple sculptures allowed artists to increase their commercial productivity.
[1] Huskinson, L. (2018). Architecture and the Mimetic Self , Routeledge. Retrieved from https://books.google.com/books?id=6HRUDwAAQBAJ&pg=PT172&lpg=PT172&dq=To+bring+our+arguments+home,+imagine+for+a+moment+a+giddy,&source=bl&ots=YBcS0hz0Co&sig=ACfU3U1bgiqcqQDrC-TfdjTY238YJQBs2A&hl=en&sa=X&ved=2ahUKEwj2zfK40I_iAhW0MX0KHentBPUQ6AEwCXoECAgQAQ#v=onepage&q=To%20bring%20our%20arguments%20home%2C%20imagine%20for%20a%20moment%20a%20giddy%2C&f=false
[2] Retrieved from https://www.nga.gov/collection/art-object-page.1005.html
[3] Retrieved from https://outlook.wustl.edu/2008/fall/hosmer.htm
[4] Bradford, R. (1912). The Life and Works of Harriet Hosmer, The American Sculptor, The New England Magazine , Vol 45. P. 268.
[5] Buick, K. (2010). Child of the Fire: Mary Edmonia Lewis and the Problem of Art History’s Black and Indian Subject, Duke University Press, p. 111.
[6] Retrieved from https://americanart.si.edu/artwork/death-cleopatra-33878
[7] Retrieved from https://americanart.si.edu/artwork/laura-brown-27650
[8] Payne, E. (1971). Anne Whitney: Art and Social Justice. The Massachusetts Review, 12 (2), 245-260. Retrieved June 12, 2020, from www.jstor.org/stable/25088108
[9] Retrieved from https://www.sealaskaheritage.org/sites/default/files/Sealaska%20Heritage%20Formline%20Art%20Kit%20ONLINE%20low%20res.pdf
[10] Retrieved from https://www.amnh.org/exhibitions/totems-to-turquoise/master-artists/charles-edenshaw


4: Emergent Topics in Neuroscience
As a discipline, neuroscience encompasses the entire range of biology from genetics and molecules to system level approaches to understanding neurons and the brain. Often this means that neuroscientists are finding new and previously unsuspected influences on how neurons function, and therefore affect behaviour. This unit highlights some of the exciting areas of neuroscience that have emerged over the past decade that promise to give the discipline new avenues of research for the next generation of neuroscientists.
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- 4.1: The Gut Microbiome and its Impact on the Brain
- Specifically, within all fields of biology there is an emerging theme that an organ (such as skin) can be colonized by different types of microbes and this colonization does not have to be homogeneous across a particular organ. Although many of these gut bacteria can be treated pharmacologically in order for them to be eliminated, this may not be always be the best treatment.
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- 4.2: Gut Microbiome and the Brain
- There are several ways in which the gut microbiota interacts with the brain. Components of bacteria, such as lipopolysaccharides, activate the innate immune system. In dysbiosis, the innate immune system is overactive, which may result in inflammation of the central nervous system. Certain bacterially-derived metabolites, such as D-lactic acid and ammonia, have also been found to have neurotoxic effects. Many gut bacteria interact with the brain through the production of neurotransmitters.
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- 4.3: Exercise and the Brain
- It has now been established that exercise, even among minimal commitment exercise routines, has an array of robust effects on the brain, such as enhanced memory, mood, cognitive functioning, plasticity, and learning capabilities. Most notably, exercise has been implicated in having anti-depressant effects and counteracting disease or age-related mental impairment and atrophy, such as Alzheimer’s disease or dementia.
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- 4.4: Integrative and Contemplative Neuroscience
- A new field of scientific study, contemplative science, is concerned with how training the mind through meditation can induce neuroplasticity. In this chapter, we explore how contemplative practices, such as mindfulness meditation, influence neural activity and the architecture of the brain. Contemplative practices involve training a complex array of cognitive processing, including attentional and emotional regulation. In this chapter, we will take a closer look at this methodology.


10: Landscape
Landscape Drawing
Drawing or painting our surroundings is something artists have done for thousands of years. Most of the ancient images of landscapes are lost forever along with the plaster walls or other supports used in their creation. Some early paintings survive decorating the walls of palaces and rooms found in areas of volcanic activity in the ancient cities of Thera and Pompeii. These dwellings were buried in volcanic ash preserving the beautiful frescoes of flora and fauna. Additionally, during the Amarna Period in Egypt there was a flourishing of artistic activity unlike any the Ancient Egyptians previously experienced. Some of the artwork depicted natural scenes similar to landscapes with vitality and life.
LANDSCAPE FROM 3,500 YEARS AGO!
Island of Thera, Minoan 2000 - 1400 BCE
https://kuscholarworks.ku.edu/bitstream/handle/1808/10273/King_ku_0099M_12275_DATA_1.pdf;sequence=1
https://www.cs.princeton.edu/courses/archive/spring07/cos598C/notes/4_feb_2007_presentation.pdf
Amarna Landscape 1353-1336 BCE
https://www.amarnaproject.com/pages/amarna_the_place/north_palace/index.shtml
https://www.britannica.com/art/Amarna-style
DETAIL OF FLEMISH LANDSCAPE FROM 1500s
NORTHERN RENAISSANCE LANDSCAPE
• Take a look at this early Flemish 1500s painting of a landscape
• What areas can you identify that help create the illusion of depth?
• Some of these are known as Principles of Design, others are Art Elements
• There are also three distinct areas of the landscape explained below
IDENTIFIABLE LANDSCAPE PARTS
• Take a look at this 1800s painting of a landscape
• What areas can you identify that help create the illusion of depth?
• There are also three distinct areas of the landscape – can you name these three areas?
• Answer below
Answer: FOREGROUND, MIDDLE GROUND, AND BACKGROUND
• Foreground is in yellow
• Middle ground is in blue
• Background is in violet
OTHER FACTORS
• Notice that the landscape features a full range of values
• The shapes with the highest contrast are closest to the viewer in the foreground
• The Principle of Verticality is the landscape forms closest to us are located at the bottom of the visual field (area of the paper if a drawing, canvas if a painting)
• The middle ground has less contrast and detail
• The background has the least amount of contrast giving the illusion that the shapes “fade into the distance”
• In a painting, the intensity of color may be brighter in the foreground and become less intense (more dull/diluted) in the middle and backgrounds
“RULE OF THIRDS”
• Rule of Thirds is dividing the visual field into thirds
• Divisions into thirds can be horizontal, vertical, or both
• It does not have to be exact, since it is an aesthetic design principle
• Rule of Thirds applies nicely to landscape photography, painting, and drawing
• The concept of the Rule of Thirds is a Principle of Design
EXAMPLES OF 2-D ART USING RULE OF THIRDS LANDSCAPE FORMAT
EXAMPLE OF RULE OF THIRDS PORTRAIT FORMAT
VERTICAL RULE OF THIRDS MAY RELATE TO FOREGROUND, MIDDLE GROUND, AND BACKGROUND
• The foreground is made up of the large rocks
• The middle ground features the closest trees
• The background includes the lightest in value trees - fading them into the background
CONTEMPORARY DRAWING
1500s DUTCH/FLEMISH PAINTING
NOT ALWAYS RULE OF THIRDS
• This painting creates balance through asymmetrical placement of the sailboats
• Other important factors include the use of light and shadow, repetition of forms (boat sails), shape of the clouds, and the placement of the horizon line
LATE 1700S/EARLY 1800s BRITISH PAINTING
EARLY 1800s BRITISH PAINTING
EARLY-MID 1800s FRENCH PAINTING
MID-LATE 1800s FRENCH PAINTING
MID-LATE 1800s AMERICAN PAINTING
MID-1900s AMERICAN
LANDSCAPE DRAWINGS INCLUDING BUILDINGS
CITYSCAPES
If you include a building in your landscape, looking at these next several cityscape slides may help you
Student Work
Landscape Drawing Assignment
Where to Begin?
• Choose a place outside to draw where you can view a natural setting
• If you successfully include a building that’s extra credit
• Determine your eye level
• Can you include a foreground, middle ground, and background?
• Create a balanced composition by cropping
• Possibly use “Rule of Thirds” to create balance
• Use softer pencils from HB up to 6B and a full sheet of paper
• Hold the pencil loosely and relax
• Focus on values


6.1.1: Simple and Compound Interest (Exercises)
SECTION 6.1 PROBLEM SET: SIMPLE INTEREST AND DISCOUNT
Do the following simple interest problems.
| 1) If an amount of $2,000 is borrowed at a simple interest rate of 10% for 3 years, how much is the interest? | 2) You borrow $4,500 for six months at a simple interest rate of 8%. How much is the interest? |
| 3) John borrows $2400 for 3 years at 9% simple interest. How much will he owe at the end of 3 years? | 4) Jessica takes a loan of $800 for 4 months at 12% simple interest. How much does she owe at the end of the 4-month period? |
| 5) If an amount of $2,160, which includes a 10% simple interest for 2 years, is paid back, how much was borrowed 2 years earlier? | 6) Jamie just paid off a loan of $2,544, the principal and simple interest. If he took out the loan six months ago at 12% simple interest, what was the amount borrowed? |
| 7) Shanti charged $800 on her charge card and did not make a payment for six months. If there is a monthly charge of 1.5%, how much does she owe? | 8) A credit card company charges 18% interest on the unpaid balance. If you owed $2000 three months ago and have been delinquent since, how much do you owe? |
SECTION 6.1 PROBLEM SET: SIMPLE INTEREST AND DISCOUNT
Do the following simple interest problems.
| 9) An amount of $2000 is borrowed for 3 years. At the end of the three years, $2660 is paid back. What was the simple interest rate? | 10) Nancy borrowed $1,800 and paid back $1,920, four months later. What was the simple interest rate? |
| 11) Jose agrees to pay $2,000 in one year at an interest rate of 12%. The bank subtracts the discount of 12% of $2,000, and gives the rest to Jose. Find the amount of the discount and the proceeds to Jose. | 12) Tasha signs a note for a discounted loan agreeing to pay $1200 in 8 months at an 18% discount rate. Determine the amount of the discount and the proceeds to her. |
| 13) An amount of $8,000 is borrowed at a discount rate of 12%, find the proceeds if the length of the loan is 7 months. | 14) An amount of $4,000 is borrowed at a discount rate of 10%, find the proceeds if the length of the loan is 180 days. |
| 15) Derek needs $2400 new equipment for his shop. He can borrow this money at a discount rate of 14% for a year. Find the amount of the loan he should ask for so that his proceeds are $2400. | 16) Mary owes Jim $750, and wants to repay him. Mary decides to borrow the amount from her bank at a discount rate of 16%. If she borrows the money for 10 months, find the amount of the loan she should ask for so that her proceeds are $750? |
SECTION 6.1 PROBLEM SET: COMPOUND INTEREST
Do the following compound interest problems involving a lump-sum amount.
| 17) What will the final amount be in 4 years if $8,000 is invested at 9.2% compounded monthly.? |
18) How much should be invested at 10.3% for it
|
|
19) Lydia's aunt Rose left her $5,000. Lydia spent $1,000 on her wardrobe and deposited the rest
|
20) Thuy needs $1,850 in eight months for her college tuition. How much money should she deposit lump sum in an account paying 8.2% compounded monthly to achieve that goal? |
|
21) Bank A pays 5% compounded daily, while
|
22) EZ Photo Company needs five copying machines in 2 1/2 years for a total cost of $15,000. How much money should be deposited now to pay for these machines, if the interest rate is 8% compounded semiannually? |
| 23) Jon's grandfather planned to give him $12,000 in 10 years. Jon has convinced his grandfather to pay him $6,000 now, instead. If Jon invests this $6,000 at 7.5% compounded continuously, how much money will he have in 10 years? | 24) What will be the price of a $20,000 car in 5 years if the inflation rate is 6%? |
SECTION 6.1 PROBLEM SET: COMPOUND INTEREST
Do the following compound interest problems.
| 25) At an interest rate of 8% compounded continuously, how many years will it take to double your money? | 26) If an investment earns 10% compounded continuously, in how many years will it triple? |
| 27) The City Library ordered a new computer system costing $158,000; it will be delivered in 6 months, and the full amount will be due 30 days after delivery. How much must be deposited today into an account paying 7.5% compounded monthly to have $158,000 in 7 months? | 28) Mr. and Mrs. Tran is expecting a baby girl in a few days. They want to put away money for her college education now. How much money should they deposit in an account paying 10.2% so they will have $100,000 in 18 years to pay for their daughter's educational expenses? |
| 29) Find the effective interest rate for an account paying 7.2% compounded quarterly. | 30) If a bank pays 5.75% compounded monthly, what is the effective interest rate? |
|
31) The population of the African nation of Cameroon was 12 million people in the year 2015; it has been growing at a rate of 2.5% per year. If the population continues to grows at a rate, what will the population be in 2030?
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32) According to the Law of 72, if an amount grows at an annual rate of 1%, then it doubles every seventy-two years. Suppose a bank pays 5% interest, how long will it take for you to double your money? How about at 15%? |


1.2: Teaching Philosophy
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There are many different ways to teach, varying circumstances to take into account, and philosophies to apply to each classroom. And what better way to have a positive impact on the world than to offer knowledge for consumption? The term ‘teacher’ can be applied to anyone who imparts knowledge of any topic, but it is generally more focused on those who are hired to do so (teach, n.d., n.p.). In imparting knowledge to our students, it is inevitable that we must consider our own personal philosophies, or pedagogies, and determine not only how we decide what our philosophies are, but also how those impact our consumers.
Horace Mann, from Report of the Massachusetts Board of Education (1848)
Horace Mann (May 4, 1796 – August 2, 1859) was an American educational reformer known for his commitment to promoting public education.
Without undervaluing any other human agency, it may be safely affirmed that the common school, improved and energized as it can easily be, may become the most effective and benignant of all the forces of civilization. Two reasons sustain this position. In the first place, there is an universality in its operation, which can be affirmed of no other institution whatever. If administered in the spirit of justice and conciliation, all the rising generation may be brought within the circle of its reformatory and elevating influences. And, in the second place, the materials upon which it operates are so pliant and ductile as to be susceptible of assuming a greater variety of forms than any other earthly work of the Creator. . . .
According to the European theory, men are divided into classes-some to toil and earn, others to seize and enjoy. According to the Massachusetts theory, all are to have an equal chance for earning, and equal security in the enjoyment of what they earn. A republican form of government, without intelligence in the people, must be, on a vast scale, what a mad-house without superintendent or keepers would be on a small one. . . . However elevated the moral character of a constituency may be, however, well-informed in matters of general science or history, yet they must, if citizens of a republic, understand something of the true nature and functions of the government under which they live. . . .
The establishment of a republican government, without well-appointed and efficient means for the universal education of the people, is the most rash and foolhardy experiment ever tried by man. . . . It may be an easy thing to make a republic, but it a very laborious thing to make republicans; and woe to the republic that rests upon no better foundations than ignorance, selfishness, and passion! . . .
Such, then, . . . is the Massachusetts system of common schools. Reverently it recognizes and affirms the sovereign rights of the Creator, sedulously and sacredly it guards the religious rights of the creature. . . . In a social and political sense, it is a free school system. It knows no distinction of rich and poor, of bond and free, or between those, who, in the imperfect light of this world, are seeking, through different avenues, to reach the gate of heaven. Without money and without price, it throws open its doors, and spreads the table of its bounty, for all the children of the State. Like the sun, it shines not only upon the good, but upon the evil, that they may become good; and, like the rain, its blessings descend not only upon the just, but upon the unjust, that their injustice may depart from them, and be know no more.
In order to develop a teaching philosophy, a teacher should examine and continuously reflect on the following:
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, ORIGINAL
PUBLIC DOMAIN CONTENT


10.2: Color Mixtures
Lesson
Let's see what color-mixing has to do with ratios.
Exercise \(\PageIndex{1}\): Number Talk: Adjusting a Factor
Find the value of each product mentally.
\(6\cdot 15\)
\(12\cdot 15\)
\(6\cdot 45\)
\(13\cdot 45\)
Exercise \(\PageIndex{2}\): Turning Green
- In the left cylinder, mix 5 ml of blue and 15 ml of yellow. This is a single batch of green.
-
Suppose you have one batch of green but want to make more. Which of the following would produce the same shade of green?
If you're unsure, try creating the mixture in the right cylinder. Start with the amounts in a single batch (5 ml of blue and 15 ml of yellow) and . . .- add 20 ml of blue and 20 ml of yellow
- double the amount of blue and the amount of yellow
- triple the amount of blue and the amount of yellow
- mix a single batch with a double batch
- double the amount of blue and triple the amount of yellow
- For one of the mixtures that produces the same shade, write down the number of ml of blue and yellow used in the mixture.
- For the same mixture that produces the same shade, draw a diagram of the mixture. Make sure your diagram shows the number of milliliters of blue, yellow, and the number of batches.
- Someone was trying to make the same shade as the original single batch, but started by adding 20 ml of blue and 20 ml of yellow. How can they add more but still create the same shade of green?
- Invent a recipe for a bluer shade of green. Write down the amounts of yellow and blue that you used, and draw a diagram. Explain how you know it will be bluer than the original single batch of green before testing it out.
Are you ready for more?
Someone has made a shade of green by using 17 ml of blue and 13 ml of yellow. They are sure it cannot be turned into the original shade of green by adding more blue or yellow. Either explain how more can be added to create the original green shade, or explain why this is impossible.
Exercise \(\PageIndex{3}\): Perfect Purple Water
The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.”
Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water.
- Which person will get a color mixture that is the same shade as Perfect Purple Water? Explain or show your reasoning.
- Find another combination of blue water and red water that will also result in the same shade as Perfect Purple Water. Explain or show your reasoning.
Summary
When mixing colors, doubling or tripling the amount of each color will create the same shade of the mixed color. In fact, you can always multiply the amount of each color by the same number to create a different amount of the same mixed color.
For example, a batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint.
- To make two batches of dark orange paint, we can mix 8 ml of red paint with 4 ml of yellow paint.
- To make three batches of dark orange paint, we can mix 12 ml of red paint with 6 ml of yellow paint.
Here is a diagram that represents 1, 2, and 3 batches of this recipe.
We say that the ratios \(4:2\), \(8:4\), and \(12:6\) are equivalent because they describe the same color mixture in different numbers of batches, and they make the same shade of orange.
Practice
Exercise \(\PageIndex{4}\)
Here is a diagram showing a mixture of red paint and green paint needed for 1 batch of a particular shade of brown.
Add to the diagram so that it shows 3 batches of the same shade of brown paint.
Exercise \(\PageIndex{5}\)
Diego makes green paint by mixing 10 tablespoons of yellow paint and 2 tablespoons of blue paint. Which of these mixtures produce the same shade of green paint as Diego’s mixture? Select all that apply.
- For every 5 tablespoons of blue paint, mix in 1 tablespoon of yellow paint.
- Mix tablespoons of blue paint and yellow paint in the ratio \(1:5\).
- Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.
- Mix 11 tablespoons of yellow paint and 3 tablespoons of blue paint.
- For every tablespoon of blue paint, mix in 5 tablespoons of yellow paint.
Exercise \(\PageIndex{6}\)
To make 1 batch of sky blue paint, Clare mixes 2 cups of blue paint with 1 gallon of white paint.
- Explain how Clare can make 2 batches of sky blue paint.
- Explain how to make a mixture that is a darker shade of blue than the sky blue.
- Explain how to make a mixture that is a lighter shade of blue than the sky blue.
Exercise \(\PageIndex{7}\)
A smoothie recipe calls for 3 cups of milk, 2 frozen bananas and 1 tablespoon of chocolate syrup.
- Create a diagram to represent the quantities of each ingredient in the recipe.
- Write 3 different sentences that use a ratio to describe the recipe.
(From Unit 2.1.2)
Exercise \(\PageIndex{8}\)
Write the missing number under each tick mark on the number line.
(From Unit 2.1.1)
Exercise \(\PageIndex{9}\)
Find the area of the parallelogram. Show your reasoning.
(From Unit 1.2.1)
Exercise \(\PageIndex{10}\)
Complete each equation with a number that makes it true.
- \(11\cdot\frac{1}{4}=\underline{\qquad}\)
- \(7\cdot\frac{1}{4}=\underline{\qquad}\)
- \(13\cdot\frac{1}{27}=\underline{\qquad}\)
- \(13\cdot\frac{1}{99}=\underline{\qquad}\)
- \(x\cdot\frac{1}{y}=\underline{\qquad}\)
(As long as \(y\) does not equal 0.)
(From Unit 2.1.1)


3.3: Research and Other Types of Source-based Writing
The fact that we don’t have quite enough different words to express all possible variations of information-gathering tasks has created an area of potential confusion for students writing research papers for English classes. The following paragraph is designed to clear that up, so please read it carefully.
Figure \(\PageIndex{1}\)
Some high school and first-year college writing courses use the term “research paper” or “research writing” to apply to any situation in which students use information from an outside source in writing a paper. The logic behind this is that if the writer has to go find information from a source, that action of going and finding information is similar to research, so it is convenient to call that kind of writing task a “research paper.” However, it is only true research if it starts from a QUESTION to which the writer genuinely doesn’t know the answer and if the writer then develops or builds the answer to the question through gathering and processing information.
To help keep that difference in mind, this module will use “ research ” to refer to the goal-directed process of gathering information and building the answer to a research question, and “ source-based writing ” to refer to the many other types of information gathering and source-based writing one might do.
Figure \(\PageIndex{2}\)
One important indicator of the difference between research and other source-based writing tasks is when in the process you develop the thesis (main point) of your paper. In a research project, you begin with a question, gather the data from which you will derive or build the answer to the question, build the answer, and then state your answer in a single sentence. This one-sentence statement of your answer to your research question then becomes your thesis statement and serves as the main point of your paper. In the research writing process, therefore, stating your thesis happens at the pivot point between research and writing (so roughly half or two thirds of the way through the project, depending on the amount of time spent gathering and processing information).
Any assignment for which you begin by developing your thesis and then go out and gather information to support it is indeed be a source-based writing assignment, but it is not technically research because it begins from the answer instead of the question.
Being aware of this distinction is essential to your successful completion of both research projects and other source-based writing tasks. The work processes that lead to efficiency and success with research projects are very different from the work processes you may have used successfully for other types of source-based papers. Both offer valuable learning experiences, but it is important to understand which type of assignment you are being asked to do so that you can adjust your expectations accordingly.
Think of the most recent writing project you have done that required sources. Based on this definition, was it a research project or a source-based writing project?


4.4: Other Summaries
- Create and interpret stemplots, line graphs, time series for univariate data.
- Create and interpret contingency tables and scatter plots for bivariate data.
Stem-and-Leaf Diagrams or Stemplots
One simple graph, the stem-and-leaf graph or stemplot , comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two. Likewise, the number 5,432 has stem 543 and leaf two. The decimal 9.3 has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.
For Susan Dean's spring pre-calculus class, scores for the first exam were as follows (smallest to largest):
33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100
| Stem | Leaf |
|---|---|
| 3 | 3 |
| 4 | 2 9 9 |
| 5 | 3 5 5 |
| 6 | 1 3 7 8 8 9 9 |
| 7 | 2 3 4 8 |
| 8 | 0 3 8 8 8 |
| 9 | 0 2 4 4 4 4 6 |
| 10 | 0 |
The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% \(\left(\frac{8}{31}\right)\) were in the 90s or 100, a fairly high number of As.
For the Park City basketball team, scores for the last 30 games were as follows (smallest to largest):
32; 32; 33; 34; 38; 40; 42; 42; 43; 44; 46; 47; 47; 48; 48; 48; 49; 50; 50; 51; 52; 52; 52; 53; 54; 56; 57; 57; 60; 61
Construct a stem plot for the data.
- Answer
-
Stem Leaf 3 2 2 3 4 8 4 0 2 2 3 4 6 7 7 8 8 8 9 5 0 0 1 2 2 2 3 4 6 7 7 6 0 1
The stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later.
The data are the distances (in kilometers) from a home to local supermarkets. Create a stemplot using the data:
1.1; 1.5; 2.3; 2.5; 2.7; 3.2; 3.3; 3.3; 3.5; 3.8; 4.0; 4.2; 4.5; 4.5; 4.7; 4.8; 5.5; 5.6; 6.5; 6.7; 12.3
Do the data seem to have any concentration of values?
HINT: The leaves are to the right of the decimal.
Answer
The value 12.3 may be an outlier. Values appear to concentrate at three and four kilometers.
| Stem | Leaf |
|---|---|
| 1 | 1 5 |
| 2 | 3 5 7 |
| 3 | 2 3 3 5 8 |
| 4 | 0 2 5 5 7 8 |
| 5 | 5 6 |
| 6 | 5 7 |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
| 11 | |
| 12 | 3 |
The following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data and identify any outliers:
0.5; 0.7; 1.1; 1.2; 1.2; 1.3; 1.3; 1.5; 1.5; 1.7; 1.7; 1.8; 1.9; 2.0; 2.2; 2.5; 2.6; 2.8; 2.8; 2.8; 3.5; 3.8; 4.4; 4.8; 4.9; 5.2; 5.5; 5.7; 5.8; 8.0
- Answer
-
Stem Leaf 0 5 7 1 1 2 2 3 3 5 5 7 7 8 9 2 0 2 5 6 8 8 8 3 5 8 4 4 8 9 5 2 5 7 8 6 7 8 0 The value 8.0 may be an outlier. Values appear to concentrate at one and two miles.
A side-by-side stem-and-leaf plot allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems. Tables \(\PageIndex{1}\) and \(\PageIndex{2}\) show the ages of presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data.
| President | Ageat Inauguration | President | Age | President | Age |
|---|---|---|---|---|---|
| Pierce | 48 | Harding | 55 | Obama | 47 |
| Polk | 49 | T. Roosevelt | 42 | G.H.W. Bush | 64 |
| Fillmore | 50 | Wilson | 56 | G. W. Bush | 54 |
| Tyler | 51 | McKinley | 54 | Reagan | 69 |
| Van Buren | 54 | B. Harrison | 55 | Ford | 61 |
| Washington | 57 | Lincoln | 52 | Hoover | 54 |
| Jefferson | 57 | Grant | 46 | Truman | 60 |
| Madison | 57 | Hayes | 54 | Eisenhower | 62 |
| J. Q. Adams | 57 | Arthur | 51 | L. Johnson | 55 |
| Monroe | 58 | Garfield | 49 | Kennedy | 43 |
| J. Adams | 61 | A. Johnson | 56 | F. Roosevelt | 51 |
| Jackson | 61 | Cleveland | 47 | Nixon | 56 |
| Taylor | 64 | Taft | 51 | Clinton | 47 |
| Buchanan | 65 | Coolidge | 51 | Trump | 70 |
| W. H. Harrison | 68 | Cleveland | 55 | Carter | 52 |
| President | Age | President | Age | President | Age |
|---|---|---|---|---|---|
| Washington | 67 | Lincoln | 56 | Hoover | 90 |
| J. Adams | 90 | A. Johnson | 66 | F. Roosevelt | 63 |
| Jefferson | 83 | Grant | 63 | Truman | 88 |
| Madison | 85 | Hayes | 70 | Eisenhower | 78 |
| Monroe | 73 | Garfield | 49 | Kennedy | 46 |
| J. Q. Adams | 80 | Arthur | 56 | L. Johnson | 64 |
| Jackson | 78 | Cleveland | 71 | Nixon | 81 |
| Van Buren | 79 | B. Harrison | 67 | Ford | 93 |
| W. H. Harrison | 68 | Cleveland | 71 | Reagan | 93 |
| Tyler | 71 | McKinley | 58 | ||
| Polk | 53 | T. Roosevelt | 60 | ||
| Taylor | 65 | Taft | 72 | ||
| Fillmore | 74 | Wilson | 67 | ||
| Pierce | 64 | Harding | 57 | ||
| Buchanan | 77 | Coolidge | 60 |
Answer
| Ages at Inauguration | Ages at Death | |
|---|---|---|
| 9 9 8 7 7 7 6 3 2 | 4 | 6 9 |
| 8 7 7 7 7 6 6 6 5 5 5 5 4 4 4 4 4 2 1 1 1 1 1 0 | 5 | 3 6 6 7 7 8 |
| 9 5 4 4 2 1 1 1 0 | 6 | 0 0 3 3 4 4 5 6 7 7 7 8 |
| 7 | 0 0 1 1 1 4 7 8 8 9 | |
| 8 | 0 1 3 5 8 | |
| 9 | 0 0 3 3 |
The table shows the number of wins and losses the Atlanta Hawks have had in 42 seasons. Create a side-by-side stem-and-leaf plot of these wins and losses.
| Losses | Wins | Year | Losses | Wins | Year |
|---|---|---|---|---|---|
| 34 | 48 | 1968–1969 | 41 | 41 | 1989–1990 |
| 34 | 48 | 1969–1970 | 39 | 43 | 1990–1991 |
| 46 | 36 | 1970–1971 | 44 | 38 | 1991–1992 |
| 46 | 36 | 1971–1972 | 39 | 43 | 1992–1993 |
| 36 | 46 | 1972–1973 | 25 | 57 | 1993–1994 |
| 47 | 35 | 1973–1974 | 40 | 42 | 1994–1995 |
| 51 | 31 | 1974–1975 | 36 | 46 | 1995–1996 |
| 53 | 29 | 1975–1976 | 26 | 56 | 1996–1997 |
| 51 | 31 | 1976–1977 | 32 | 50 | 1997–1998 |
| 41 | 41 | 1977–1978 | 19 | 31 | 1998–1999 |
| 36 | 46 | 1978–1979 | 54 | 28 | 1999–2000 |
| 32 | 50 | 1979–1980 | 57 | 25 | 2000–2001 |
| 51 | 31 | 1980–1981 | 49 | 33 | 2001–2002 |
| 40 | 42 | 1981–1982 | 47 | 35 | 2002–2003 |
| 39 | 43 | 1982–1983 | 54 | 28 | 2003–2004 |
| 42 | 40 | 1983–1984 | 69 | 13 | 2004–2005 |
| 48 | 34 | 1984–1985 | 56 | 26 | 2005–2006 |
| 32 | 50 | 1985–1986 | 52 | 30 | 2006–2007 |
| 25 | 57 | 1986–1987 | 45 | 37 | 2007–2008 |
| 32 | 50 | 1987–1988 | 35 | 47 | 2008–2009 |
| 30 | 52 | 1988–1989 | 29 | 53 | 2009–2010 |
- Answer
-
Table \(\PageIndex{A}\): Atlanta Hawks Wins and Losses Number of Wins Number of Losses 3 1 9 9 8 8 6 5 2 5 5 9 8 7 6 6 5 5 4 3 1 1 1 1 0 3 0 2 2 2 2 4 4 5 6 6 6 9 9 9 8 8 7 6 6 6 3 3 3 2 2 1 1 0 4 0 0 1 1 2 4 5 6 6 7 7 8 9 7 7 6 3 2 0 0 0 0 5 1 1 1 2 3 4 4 6 7 6 9
Line Graphs or Frequency Polygons
Another type of graph that is useful for specific data values is a line graph or a frequency polygon . In the particular line graph shown in the example below, the x -axis (horizontal axis) consists of data values and the y -axis (vertical axis) consists of frequency points . The frequency points are connected using line segments.
In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in Table and in Figure.
| Number of times teenager is reminded | Frequency |
|---|---|
| 0 | 2 |
| 1 | 5 |
| 2 | 8 |
| 3 | 14 |
| 4 | 7 |
| 5 | 4 |
In a survey, 40 people were asked how many times per year they had their car in the shop for repairs. The results are shown in Table. Construct a line graph.
| Number of times in shop | Frequency |
|---|---|
| 0 | 7 |
| 1 | 10 |
| 2 | 14 |
| 3 | 9 |
Answer
Frequency polygons can also be used for comparing distributions. This is achieved by overlaying the frequency polygons drawn for different data sets.
We will construct an overlay frequency polygon comparing the final exam scores with the students’ final numeric grade.
| Range | Midpoint | Frequency | Cumulative Frequency |
|---|---|---|---|
| 49.5-59.5 | 54.5 | 5 | 5 |
| 59.5-69.5 | 64.5 | 10 | 15 |
| 69.5-79.5 | 74.5 | 30 | 45 |
| 79.5-89.5 | 84.5 | 40 | 85 |
| 89.5-99.5 | 94.5 | 15 | 100 |
| Range | Midpoint | Frequency | Cumulative Frequency |
|---|---|---|---|
| 49.5-59.5 | 54.5 | 10 | 10 |
| 59.5-69.5 | 64.5 | 10 | 20 |
| 69.5-79.5 | 74.5 | 30 | 50 |
| 79.5-89.5 | 84.5 | 45 | 95 |
| 89.5-99.5 | 94.5 | 5 | 100 |
Time Series Graphs
Suppose that we want to study the temperature range of a region for an entire month. Every day at noon we note the temperature and write this down in a log. A variety of statistical studies could be done with this data. We could find the mean or the median temperature for the month. We could construct a histogram displaying the number of days that temperatures reach a certain range of values. However, all of these methods ignore a portion of the data that we have collected.
One feature of the data that we may want to consider is that of time. Since each date is paired with the temperature reading for the day, we don't have to think of the data as being random. We can instead use the times given to impose a chronological order on the data. A graph that recognizes this ordering and displays the changing temperature as the month progresses is called a time series graph.
To construct a time series graph, we must look at both pieces of our paired data set . We start with a standard Cartesian coordinate system. The horizontal axis is used to plot the date or time increments, and the vertical axis is used to plot the values of the variable that we are measuring. By doing this, we make each point on the graph correspond to a date and a measured quantity. The points on the graph are typically connected by straight lines in the order in which they occur.
The following data shows the Annual Consumer Price Index, each month, for ten years. Construct a time series graph for the Annual Consumer Price Index data only.
| Year | Jan | Feb | Mar | Apr | May | Jun | Jul |
|---|---|---|---|---|---|---|---|
| 2003 | 181.7 | 183.1 | 184.2 | 183.8 | 183.5 | 183.7 | 183.9 |
| 2004 | 185.2 | 186.2 | 187.4 | 188.0 | 189.1 | 189.7 | 189.4 |
| 2005 | 190.7 | 191.8 | 193.3 | 194.6 | 194.4 | 194.5 | 195.4 |
| 2006 | 198.3 | 198.7 | 199.8 | 201.5 | 202.5 | 202.9 | 203.5 |
| 2007 | 202.416 | 203.499 | 205.352 | 206.686 | 207.949 | 208.352 | 208.299 |
| 2008 | 211.080 | 211.693 | 213.528 | 214.823 | 216.632 | 218.815 | 219.964 |
| 2009 | 211.143 | 212.193 | 212.709 | 213.240 | 213.856 | 215.693 | 215.351 |
| 2010 | 216.687 | 216.741 | 217.631 | 218.009 | 218.178 | 217.965 | 218.011 |
| 2011 | 220.223 | 221.309 | 223.467 | 224.906 | 225.964 | 225.722 | 225.922 |
| 2012 | 226.665 | 227.663 | 229.392 | 230.085 | 229.815 | 229.478 | 229.104 |
| Year | Aug | Sep | Oct | Nov | Dec | Annual |
|---|---|---|---|---|---|---|
| 2003 | 184.6 | 185.2 | 185.0 | 184.5 | 184.3 | 184.0 |
| 2004 | 189.5 | 189.9 | 190.9 | 191.0 | 190.3 | 188.9 |
| 2005 | 196.4 | 198.8 | 199.2 | 197.6 | 196.8 | 195.3 |
| 2006 | 203.9 | 202.9 | 201.8 | 201.5 | 201.8 | 201.6 |
| 2007 | 207.917 | 208.490 | 208.936 | 210.177 | 210.036 | 207.342 |
| 2008 | 219.086 | 218.783 | 216.573 | 212.425 | 210.228 | 215.303 |
| 2009 | 215.834 | 215.969 | 216.177 | 216.330 | 215.949 | 214.537 |
| 2010 | 218.312 | 218.439 | 218.711 | 218.803 | 219.179 | 218.056 |
| 2011 | 226.545 | 226.889 | 226.421 | 226.230 | 225.672 | 224.939 |
| 2012 | 230.379 | 231.407 | 231.317 | 230.221 | 229.601 | 229.594 |
Answer
The following table is a portion of a data set from www.worldbank.org. Use the table to construct a time series graph for CO 2 emissions for the United States.
| Ukraine | United Kingdom | United States | |
|---|---|---|---|
| 2003 | 352,259 | 540,640 | 5,681,664 |
| 2004 | 343,121 | 540,409 | 5,790,761 |
| 2005 | 339,029 | 541,990 | 5,826,394 |
| 2006 | 327,797 | 542,045 | 5,737,615 |
| 2007 | 328,357 | 528,631 | 5,828,697 |
| 2008 | 323,657 | 522,247 | 5,656,839 |
| 2009 | 272,176 | 474,579 | 5,299,563 |
Time series graphs are important tools in various applications of statistics. When recording values of the same variable over an extended period of time, sometimes it is difficult to discern any trend or pattern. However, once the same data points are displayed graphically, some features jump out. Time series graphs make trends easy to spot.
Bivariate Data
Earlier we discussed the methods of summarizing and organizing the data obtained from observing one variable. Such data are called univariate data . When we are interested in studying the relationship between a pair of variables we must collect and organize the data on two variables at the same time. Such data itself is called bivariate data and there are several ways to organize such data depending on the types of the variables.
|
Univariate Data |
Bivariate Data |
||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
The mileage of 5 cars
|
The ages and mileage of 5 cars
|
Scatter Plots
When both variables are quantitative, we can construct a scatter plot to organize the data. To construct a scatterplot , we use a horizontal axis for the observations of one variable and a vertical axis for the observations of the other. When picking which axis to use for each variable consider whether you suspect that one variable depends on the other. The independent variable will be on the x-axis and dependent will be on the y axis. Each pair of observations is then plotted as a point.
The summary of the ages and the mileages of a sample of 5 cars is shown below:
| Car | \(x\) (age in years) | \(y\) (mileage in miles) |
|---|---|---|
|
1 |
7 |
78524 |
|
2 |
2 |
12574 |
|
3 |
1 |
24914 |
|
4 |
5 |
65813 |
|
5 |
3 |
39824 |
Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data:
| \(X\) (hours practicing jump shot) | \(Y\) (points scored in a game) |
|---|---|
| 5 | 15 |
| 7 | 22 |
| 9 | 28 |
| 10 | 31 |
| 11 | 33 |
| 12 | 36 |
Construct a scatter plot and state if what Amelia thinks appears to be true.
- Answer
-
Figure \(\PageIndex{2}\)
Yes, Amelia’s assumption appears to be correct. The number of points Amelia scores per game goes up when she practices her jump shot more.
Contingency Tables
When we are interested in studying the relationship between a pair of variables we must collect and organize the data on two variables at the same time. Recall that such data itself is called bivariate data and there are several ways to organize such data depending on the types of the variables. Below are examples of univariate and bivariate qualitative data.
|
Univariate Data |
Bivariate Data |
||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
The colors of 5 cars
|
The color and condition of 5 cars
|
A table called contingency table can be used to organize bivariate data in which one or both variables are qualitative.
To construct the table, we arrange the observed frequencies into rows and columns. The intersection of a row and a column of a contingency table is called a cell. Each cell shows the frequency of observations that fit the description in the corresponding row and column.
|
Color\Condition |
Like new |
Used |
|---|---|---|
|
Light |
1 |
1 |
|
Dark |
1 |
2 |
Many times, it makes sense to add the column and row with the totals for each column and row and for the entire table.
|
Color\Condition |
Like new |
Used |
Total: |
|---|---|---|---|
|
Light |
1 |
1 |
2 |
|
Dark |
1 |
2 |
3 |
|
Total: |
2 |
3 |
5 |
Alternatively, the contingency table can be referred to as a two-way frequency table . Why? In the example above, cover the second and third columns and what's left can be easily seen as the frequency table for the colors of cars! Cover the second and third rows instead and what’s left can be easily seen as the frequency table for whether car conditions! Also note that every contingency table can be easily broken down into two frequency tables, but the two frequency tables cannot be combined into a contingency table if the original data is lost!
Destiny surveyed the students in her neighborhood and obtained the following data. Construct the contingency table that summarizes the school enrollment by level and type.
| Student | School level | School type |
|---|---|---|
| Student 1 | Middle School | Public |
| Student 2 | Middle School | Private |
| Student 3 | Elementary School | Public |
| Student 4 | Middle School | Public |
| Student 5 | Elementary School | Public |
| Student 6 | High School | Public |
| Student 7 | High School | Private |
| Student 8 | Middle School | Public |
| Student 9 | High School | Public |
| Student 10 | Elementary School | Public |
| Student 11 | Middle School | Private |
| Student 12 | Elementary School | Private |
| Student 13 | Elementary School | Private |
| Student 14 | Elementary School | Private |
| Student 15 | Elementary School | Private |
| Student 16 | Middle School | Private |
| Student 17 | Middle School | Private |
| Student 18 | High School | Private |
| Student 19 | Elementary School | Private |
- Answer
-
The following contingency table summarizes the school enrollment by level and type:
Public Private Total Elementary School 3 5 8 Middle School 3 4 7 High School 2 2 4 Total 8
11 19


14.12.3: Stocks
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What Are Stocks?
Stocks are a type of security that gives stockholders a share of ownership in a company. Stocks also are called “equities.”
Why do people buy stocks?
Why do companies issue stock?
What kinds of stock are there?
What are the benefits and risks of stocks?
How to buy and sell stocks
Understanding fees
Avoiding fraud
Additional information
Why Do People Buy Stocks?
Investors buy stocks for various reasons. Here are some of them:
- Capital appreciation, which occurs when a stock rises in price
- Dividend payments, which come when the company distributes some of its earnings to stockholders
- Ability to vote shares and influence the company
Why Do Companies Issue Stock?
Companies issue stock to get money for various things, which may include:
- Paying off debt
- Launching new products
- Expanding into new markets or regions
- Enlarging facilities or building new ones
What Kinds Of Stocks Are There?
There are two main kinds of stocks, common stock and preferred stock.
Common stock entitles owners to vote at shareholder meetings and receive dividends.
Preferred stockholders usually don’t have voting rights but they receive dividend payments before common stockholders do, and have priority over common stockholders if the company goes bankrupt and its assets are liquidated.
Common and preferred stocks may fall into one or more of the following categories:
- Growth stocks have earnings growing at a faster rate than the market average. They rarely pay dividends and investors buy them in the hope of capital appreciation. A start-up technology company is likely to be a growth stock.
- Income stocks pay dividends consistently. Investors buy them for the income they generate. An established utility company is likely to be an income stock.
- Value stocks have a low price-to-earnings (PE) ratio, meaning they are cheaper to buy than stocks with a higher PE. Value stocks may be growth or income stocks, and their low PE ratio may reflect the fact that they have fallen out of favor with investors for some reason. People buy value stocks in the hope that the market has overreacted and that the stock’s price will rebound.
- Blue-chip stocks are shares in large, well-known companies with a solid history of growth. They generally pay dividends.
Another way to categorize stocks is by the size of the company, as shown in its market capitalization. There are large-cap, mid-cap, and small-cap stocks. Shares in very small companies are sometimes called “microcap” stocks. The very lowest priced stocks are known as “penny stocks.” These companies may have little or no earnings. Penny stocks do not pay dividends and are highly speculative.
What Are The Benefits And Risks Of Stocks?
Stocks offer investors the greatest potential for growth (capital appreciation) over the long haul. Investors willing to stick with stocks over long periods of time, say 15 years, generally have been rewarded with strong, positive returns.
But stock prices move down as well as up. There’s no guarantee that the company whose stock you hold will grow and do well, so you can lose money you invest in stocks.
If a company goes bankrupt and its assets are liquidated, common stockholders are the last in line to share in the proceeds. The company’s bondholders will be paid first, then holders of preferred stock. If you are a common stockholder, you get whatever is left, which may be nothing.
Even when companies aren’t in danger of failing, their stock price may fluctuate up or down. Large company stocks as a group, for example, have lost money on average about one out of every three years. If you have to sell shares on a day when the stock price is below the price you paid for the shares, you will lose money on the sale.
Market fluctuations can be unnerving to some investors. A stock’s price can be affected by factors inside the company, such as a faulty product, or by events the company has no control over, such as political or market events.
Stocks usually are one part of an investor’s holdings. If you are young and saving for a long-term goal such as retirement, you may want to hold more stocks than bonds. Investors nearing or in retirement may want to hold more bonds than stocks.
The risks of stock holdings can be offset in part by investing in a number of different stocks. Investing in other kinds of assets that are not stocks, such as bonds, is another way to offset some of the risks of owning stocks.
How To Buy And Sell Stocks
You can buy and sell stocks through:
- A direct stock plan
- A dividend reinvestment plan
- A discount or full-service broker
- A stock fund
Direct stock plans. Some companies allow you to buy or sell their stock directly through them without using a broker. This saves on commissions, but you may have to pay other fees to the plan, including if you transfer shares to a broker to sell them. Some companies limit direct stock plans to employees of the company or existing shareholders. Some require minimum amounts for purchases or account levels.
Direct stock plans usually will not allow you to buy or sell shares at a specific market price or at a specific time. Instead, the company will buy or sell shares for the plan at set times — such as daily, weekly, or monthly — and at an average market price. Depending on the plan, you may be able to automate your purchases and have the cost deducted automatically from your savings account.
Dividend reinvestment plans. These plans allow you to buy more shares of a stock you already own by reinvesting dividend payments into the company. You must sign an agreement with the company to have this done. Check with the company or your brokerage firm to see if you will be charged for this service.
Discount or full-service broker. Brokers buy and sell shares for customers for a fee, known as a commission.
Stock funds are another way to buy stocks. These are a type of mutual fund that invests primarily in stocks. Depending on its investment objective and policies, a stock fund may concentrate on a particular type of stock, such as blue chips, large-cap value stocks, or mid-cap growth stocks. Stock funds are offered by investment companies and can be purchased directly from them or through a broker or adviser.
Understanding Fees
Buying and selling stocks entails fees. A direct stock plan or a dividend reinvestment plan may charge you a fee for that service. Brokers who buy and sell stocks for you charge a commission. A discount brokerage charges lower commissions than what you would pay at a full-service brokerage. But generally you have to research and choose investments by yourself. A full-service brokerage costs more, but the higher commissions pay for investment advice based on that firm’s research.
Avoiding Fraud
Stocks in public companies are registered with the SEC and in most cases, public companies are required to file reports to the SEC quarterly and annually. Annual reports include financial statements that have been audited by an independent audit firm. Information on public companies can be found on the SEC’s EDGAR system.
Additional Information
Accounts, Opening a Brokerage Account
Brokerage Orders
Buying and Selling Stock: Market Centers
Holding Your Securities
Reverse Stock Splits
Trade Execution: Rules Your Brokerage Firm Must Follow
Voting Rights-Exercise Your Voting Rights in Corporate Elections
Investor Bulletin: American Depositary Receipts
Investor Bulletin: After-Hours Trading
Contributors and Attributions
- Authored by : Investor.org. Located at : www.investor.gov/introduction-investing/basics/investment-products/stocks. License : Public Domain: No Known Copyright


35.12: A Relationship that Reflected the World Around Them
Unca Eliza Winkfield’s parents may seem to have an almost Disney-like story of falling in love but could this not be representing something bigger? While observing these chapters through a colonialism perspective, I tend to see many similarities to this story and the interactions that settlers would have with the natives. Many a time would the English take advantage of the natives through linguistics. Historically speaking, there have been many incidents where Europeans would trade land for objects to the natives at sadly low prices. In most Native tribes, land was for all people to use and not to be personally owned so this trade was thought to be great from Natives…until the Europeans would come in and make them get out with threats and actual violence. This story is to show one of the instances of how the natives were constantly being taken advantage of by the Europeans and this can be reflected between the relationship of Unca Eliza Winkfield’s parents.
“he found it not a little difficult to teach another what he yet firmly believed himself, but as we readily believe those whom we love, he was more successful than he expected, and in a little time the princess became convinced of her errors, and to good understanding help to forward her conversion” (51).
Looking at the wording here, I notice the following part: “the princess became convinced of her errors.” The word “errors” make me think how the father thinks of his wife’s religion as inferior compared to his and has to make her believe in what he sees as the correct religion. The conversion that he is aiming for is to make her more European so she can live in his society with him. But in doing so he is getting rid of some of her core beliefs and taking advantage of her love for him. You see these forms of conversions in other places in the book: whenever the daughter refers to the Natives, she says “Indians.” This term itself is problematic as the Native Americans were a highly diverse group of people that tend to be grouped all together. It reminds me of when people say similar things about how Africa is a country right? No, every tribe may have had some similarities but they all had cultures that fluctuated with each other. The relationship the parents shows the slow regression of how Native Americans were turned out to be more European as they became colonized.


13.2: The Forest Biome
The forest biome consists of close growing trees with leaf canopies that generally overlap. Much sunlight can be prevented from reaching the forest floor if tree limbs and foliage tightly intermingle. The lack of sunlight inhibits the development of undergrowth, creating an open forest structure . If the canopy is open, sunlight can reach the forest floor and promote the development of undergrowth resulting in a closed forest structure . Forests require ample amounts of annual precipitation to support their growth. The shaded conditions of the closed forest keep soils relatively moist.
Forests are found over a wide range of temperature regimes from the hot equatorial regions to the cold subarctic. Forests occupy approximately one third of Earth's land surface, but their areal extent is shrinking as humans cut the forest for material needs and economic gain.