Lesson 4

The Shape of Distributions

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Problem 1

Which of the dot plots shows a symmetric distribution?

A:
Dot plot from 9 to 20 by 1’s. Beginning at 9, number of dots above each increment is 0, 1, 1, 2, 3, 5, 6, 7, 8, 2, 1, 0.
B:
Dot plot from 9 to 20 by 1’s. Beginning at 9, number of dots above each increment is 0, 1, 1, 2, 3, 5, 3, 2, 1, 1, 0, 0.
C:
Dot plot from 1 to 12 by 1’s. Beginning at 1, number of dots above each increment is 0, 4, 0, 6, 7, 0, 3, 0, 2, 6, 5, 0.
D:
Dot plot from 1.1 to 1.9 by 0.1’s. Beginning at 1.1, number of dots above each increment is 0, 6, 4, 2, 1, 7, 11, 15, 0.

 

Solution

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Problem 2

Which of the dot plots shows a skewed distribution?

A:
Dot plot from 1.1 to 1.9 by 0.1’s. Beginning at 1.1, number of dots above each increment is 0, 6, 4, 2, 1, 1, 4, 6, 0.
B:
Dot plot from 0.5 to 6 by 0.5’s. Beginning at 0.5, number of dots above each increment is 0, 0, 0, 4, 6, 4, 1, 4, 6, 4, 0, 0.
C:
Dot plot from 9 to 18 by 1’s. Beginning at 9, number of dots above each increment is 0, 3, 5, 7, 9, 9, 7, 5, 3, 0.
D:
Dot plot from 1.1 to 2.1 by 0.1’s. Beginning at 1.1, number of dots above each increment is 0, 8, 9, 6, 4, 1, 0, 1, 0.

Solution

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Problem 3

Create a dot plot showing a uniform distribution.

Solution

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Problem 4

The data represent the number of ounces of water that 26 students drank before donating blood: 8, 8, 8, 16, 16, 16, 32, 32, 32, 32, 32, 32, 64, 64, 64, 64, 64, 64, 64, 80, 80, 80, 80, 88, 88, 88.

  1. Create a dot plot for the data.
  2. Create a box plot for the data.
  3. What information about the data is provided by the box plot that is not provided by the dot plot?
  4. What information about the data is provided by the dot plot that is not provided by the box plot?
  5. It was recommended that students drink 48 or more ounces of water. How could you use a histogram to easily display the number of students who drank the recommended amount?

Solution

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(From Unit 1, Lesson 3.)

Problem 5

The box plot represents the distribution of the number of points scored by a cross country team at 12 meets.

A boxplot from 22 to 42 by 2’s. points. Whisker from 22 to 33. Box from 35 to 38 with a vertical line at 34. Whisker from 38 to 42.
  1. If possible, find the mean. If not possible, explain why not.
  2. If possible, find the median. If not possible, explain why not.
  3. Did the cross country team ever score 30 points at a meet?

Solution

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(From Unit 1, Lesson 2.)