Lesson 4

The Shape of Data Distributions

  • Let’s explore various shapes of data.

4.1: Math Talk: Number Line Distance

Mentally, find the distance between the two values on a number line.

  • 70 and 62
  • 70 and 70
  • 70 and 79
  • 70 and 97

4.2: Suspicious Descriptions

For each picture and description:

  • Do you agree or disagree with the description?
  • If you agree, explain how you know it is correct.
  • If you disagree, explain the error and write the correct description. Explain how you know it is correct.

Bell-shaped since there is a central peak for symmetric data that is less frequent on the ends.

Histogram from 0 to 20. Bar width is 2. Heights of bars start short, get tall, and then go short again so that the right side mirrors the left side.

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Symmetric because if the distribution was cut in half, both sides would be the same shape.

Dot plot from 1 to 8 by 1’s. Beginning at 1, number of dots above each increment is 4, 7, 3, 2, 1, 1, 0, 1.

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Uniform because there seems to be the same amount of data points across the entire distribution.

Histogram from 1 to 9 by 1’s. Beginning at 1 up to but not including 2, height of bar at each interval is 1, 2, 3, 4, 5, 6, 7, 8.

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Symmetric because if the distribution was cut in half, both sides would be the same shape.

Dot plot from 0 to 4 by 1’s. Beginning at 0, number of dots above each increment is 2, 5, 3, 5, 2.

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Skewed left since most of the data is on the left side of the distribution.

Histogram from 1 to 16. Width of bar is 1. Beginning at 1 up to but not including 2, approximate height of bar at each interval is 25, 30, 37, 27, 20, 12, 15, 8, 4, 4, 0, 8, 0, 2, 4.

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4.3: Whipping Data into Shape

Describe the shape of each distribution using the terms approximately, symmetric, bell-shaped, skewed left, skewed right, uniform, or bimodal. Estimate the center of each distribution.

A

Dot plot from 20 to 80 by 20’s. 27, 1 dot. 35, 1 dot. 42, 9 dots. 51, 25 dots. 62, 9 dots. 75, 2 dots. 83, 1 dot.

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B

Histogram from 4 to 9 by 1’s. Beginning at 4 up to but not including 4 point 5, height of bar at each interval is approximately 5, 40, 50, 4, 3, 10, 35, 55, 57, 25, 3.

C

Dot plot from 10 to 50 by 10’s. Beginning at 10, number of dots above each increment is 4, 4, 4, 4, 4.

 

D

Dot plot from 0 to 18 by 1’s. Beginning at 0, number of dots above each increment is 0, 1, 3, 2, 5, 3, 4, 2, 1, 1, 2, 0, 1, 0, 1, 1, 0, 0, 1.

E

Histogram from 0 to 18 by 2’s with hash marks at 1’s. Beginning at 0 up to but not including 1, height of bar at each interval is 10, 10, 10, 9, 11, 10, 11, 11, 10, 10, 10 12, 11, 10, 10, 10, 10, 11.

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F

Histogram from 0 to 12 by 2’s with hash marks at 1’s. Beginning at 0 up to but not including 1, height of bar at each interval is 4, 8, 16, 20, 14, 10, 6, 12, 15, 19, 16, 9, 4.

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G

A dot plot from 1 to 6.

 

H

Histogram from 0 to 11. Bar width is 1. Beginning at 0 up to but not including 1, height of bar at each interval is 5, 13, 29, 26, 9, 7, 2, 0, 2.

Summary