Mean, Median, Mode and Range

Discussion through works of art encourage how to approach ambiguous and complex ideas, thoughts, and feelings. The MFAH offers a democratic space where students and teachers can develop, practice and articulate these habits of mind. Remember that the quality of the conversation is what is important, not finding the artist’s “answer.” Slow down and take the time to make careful observations. Talk about what you notice, and try to avoid jumping to conclusions and interpretations. Be sure to give enough time for silent looking and thinking.

Work of Art

Painted on the eve of World War I, Wassily Kandinsky’s wildly colored Skizze 160A (Sketch 160A) reflects the turbulence of an era unhinged by modernity and suggests an impending apocalypse. Carefully nuanced colors and seemingly erratic marks dominate this work of art. An accomplished musician, theorist, and artist, Kandinsky was intensely inspired by music. Just as the word in the title, Skizze, refers to a composer’s notes about a work in progress, the hint of musical elements and symbols infuse this work with a sense of lyricism.

 

Delicate, ethereal pastel shades illuminate the canvas, while deep blues, reds and purples stabilize the work and provide a sense of depth. The seemingly contrasting elements and the jumbled placement of figures suggest cacophony, but Kandinsky manages to achieve equilibrium and harmony in this work. Although slightly abstracted, symbols of the Apocalypse such as the horse and rider, a mountain, birds, and fish are discernible. These recognizable images bring the viewer into the painting and help interpret its mystery. The apparently haphazard structure belies the care with which Kandinsky placed each character of the composition, using different pictorial elements and moods to create an intricate balance.

 

Kandinsky believed that the artist should reveal realities of the spiritual rather than of the material world. Taking the words of composer Robert Schumann to heart—“To send light into the darkness of men’s hearts, such is the duty of the artist,”—Kandinsky believed that true artists were prophets of their age. He presented this belief of the artist as prophet in his 1912 treatise Concerning the Spiritual in Art, wherein the painter also developed an elaborate system of colors and shapes that included correlations between specific colors, emotions, and musical sounds. Just as music produces a cadence that affects the emotions and soul of its listeners, Kandinsky too believed that abstract forms and colors in the proper configuration revealed spiritual truth by enacting a vibration in the viewer’s soul. “Color is the keyboard, the eyes the hammer, the soul is the piano with many strings,” he wrote. “The artist is the hand that plays, touching one key or another purposively, to cause vibrations in the soul.”

 

Many of Kandinsky’s pre-WWI abstract canvases were inspired by the Revelation of Saint John the Divine. The rider, a common motif in his repertoire, came to signify the Horsemen of the Apocalypse, who bring epic destruction, after which the world will be redeemed. The mounted horseman became Kandinsky’s symbol of transcendence from the material to the spiritual realm. Just as apocalypse (a Greek word meaning “un-covering”) is brought by the horsemen, here it symbolizes Kandinsky’s crusade against conventional aesthetics, as a means of unveiling spiritual truths for a better future through the transformative powers of art.

Conversation

• How would you describe the composition of this work of art? Do you think there is a single focus within this work? Why or why not?
• How does the artist balance space? Compare the top section of the painting to the bottom section.
• Notice the colors. Are they warm or cool colors? How does the artist’s choice to use both warm and cool colors create a sense of chaos within the composition?
• How would this work be different if the artist only used two or three colors?
• How would you describe the tone of this work? How do the lines and shapes add to the feeling of commotion and turmoil?
• Compare the use of lines, quick lines to the thick, dark shapes. How do these contrasting elements add tension in the painting?
• Do you notice any recognizable figures or objects within the work? What clues does the artist give you as to what the objects are?

• How does the artist use contrast to suggest cacophony and discord?
• The artist was highly influenced by music. If this work was a musical piece, how do you think it would sound? How do elements from the painting add to your musical interpretation?
• While this work appears as seemingly chaotic and disorganized, there is an arrangement to its lines and marks. Describe how you believe the painting is organized.
• Even though the artist includes recognizable signs and symbols, the objects and figures are highly abstracted. What is your theory on why the artist included recognizable figures at all? Explain your reasoning.
• This work was created at the eve of World War I.  How could this work suggest an impending Apocalypse?
• The artist believed that it was the task of the artist to reveal realities of the spiritual rather than of the material world. Do you think this work achieves this goal? Justify your answer.
• A common motif within the artist’s works of art is the Horsemen of the Apocalypse, who will bring epic destruction after which the world will be redeemed. Does knowing this theme change how you interpret the work?
• Considering that this work was painted on the eve of WWI, a time in which society was struggling to come to terms with modernity. How can this work be related to the attitudes of the culture at the time?
• How can this piece be considered a hopeful message for both the future of society and art as a transformative power?

Subject Matter

In math there are different ways of communication. Students must know how to communicate their thoughts about problems through showing their work, developing charts, graphs and pictures, and answering orally.  In this assignment students are communicating their data through a chart and then developing an inference about the data through written communication.

Assessment

• In this activity, students calculate mean, median, mode and range of color data.
• Observe and list areas of color in Sketch 160A. (Example: dark blue: 3, red: 6, mustard: 3) Answers will vary according to students’ interpretations of colors. Collect data in a chart.
• Remind students of this discovery while connecting to work of art: “just as music produces a cadence that affects the emotions and soul of its listeners, Kandinsky too believed that abstract forms and colors in the proper configuration revealed spiritual truth by enacting a vibration in the viewer’s soul.”
• Use the beat of a military cadence with the following chant. This will reinforce the concepts of mean, mode, median, and range.  Teacher says, “Class, repeat after me...”

Kandinsky’s Cadence

 

See the colors the artist showed…

for mean, median, and mode....

Add the colors that are seen...

Then divide to find the Mean...

Put the numbers in a line…

Median’s the middle every time…

If 2 middles side by side...

Add middles and then divide...

The mode's the one you see often...

Find that number again and again…

The range is the next we need to know...

Solve the difference ‘tween high and low.

 

• Students use their data from chart to figure mean, median, mode, and range.

Resources

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