Lesson 15

Comparing Data Sets

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Twenty students participated in a psychology experiment which measured their heart rates in two different situations.

Dot plot from 70 to 105 by 5’s. Situation A. Beginning at 70, number of dots above each increment is 0, 1, 4, 5, 5, 4, 1, 0.
 
Dot plot from 70 to 105 by 5’s. Situation A. Beginning at 70, number of dots above each increment is 1, 2, 4, 6, 4, 2, 1, 0.
 
  1. What are the appropriate measures of center and variability to use with the data? Explain your reasoning.
  2. Which situation shows a greater typical heart rate?
  3. Which situation shows greater variability?

Problem 2

  1. Invent two situations that you think would result in distributions with similar measures of variability. Explain your reasoning.
  2. Invent two situations that you think would result in distributions with different measures of variability. Explain your reasoning.

Problem 3

The data set and some summary statistics are listed.

11.5, 12.3, 13.5, 15.6, 16.7, 17.2, 18.4, 19, 19.5, 21.5

  • mean: 16.52
  • median: 16.95
  • standard deviation: 3.11
  • IQR: 5.5
  1. How does adding 5 to each of the values in the data set impact the shape of the distribution?
  2. How does adding 5 to each of the values in the data set impact the measures of center?
  3. How does adding 5 to each of the values in the data set impact the measures of variability?

Problem 4

Here are two box plots:

Box plot from 95 to 115 by 5’s. Box plot A. Whisker from 98 to 100. Box from 100 to 109 with vertical line at 105. Whisker from 109 to 115.
Box plot from 95 to 115 by 5’s. Box plot B. Whisker from 96 to 99. Box from 99 to 111 with vertical line at 103. Whisker from 111 to 113.
  1. Which box plot has a greater median?
  2. Which box plot has a greater measure of variability?

Problem 5

The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a standard deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a standard deviation of 27 feet. 

Noah says the second lake is generally deeper than the first lake. Do you agree with Noah?

(From Algebra1, Unit 1, Lesson 13.)

Problem 6

The dot plots display the height, rounded to the nearest foot, of maple trees from two different tree farms.

Dot plot from 3 to 14 by 1's. Height in feet. Beginning at 3, number of dots above each increment is 0, 0, 0, 1, 2, 3, 2, 1, 0, 0, 0.
Dot plot from 3 to 14 by 1's. Height in feet. Beginning at 3, number of dots above each increment is 0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 0, 0.
  1. Compare the mean and standard deviation of the two data sets.
  2. What does the standard deviation tell you about the trees at these farms?
(From Algebra1, Unit 1, Lesson 12.)

Problem 7

Which box plot has an IQR of 10?

A:
Box plot from 1 to 13 by 1’s. Whisker from 1 to 1.5. Box from 1.5 to 12 with vertical line at 2. Whisker from 12 to 13.
B:
Box plot from 1 to 13 by 1’s. Whisker from 6 to 9. Box from 9 to 12 with vertical line at 10. Whisker from 12 to 13.
C:
Box plot from 1 to 13 by 1’s. Whisker from 1 to 2. Box from 2 to 12 with vertical line at 9. Whisker from 12 to 13
D:
Box plot from 1 to 13 by 1’s. Whisker from 3 to 6. Box from 6 to 9 with vertical line at 7. Whisker from 9 to 13.
(From Algebra1, Unit 1, Lesson 11.)

Problem 8

What effect does eliminating the lowest value, -6, from the data set have on the mean and median?

-6, 3, 3, 3, 3, 5, 6, 6, 8, 10

(From Algebra1, Unit 1, Lesson 9.)