The 22 students in a health class conducted an experiment in which they each recorded their pulse rates, in beats per minute, before and after completing a light exercise routine. The dot plots below display the results.

Let `s_1` and `r_1` be the standard deviation and range, respectively, of the data before exercise, and let `s_2` and `r_2` be the standard deviation and range, respectively, of the data after exercise. Which of the following is true?

Options

A. `s_1 =s_2` and `r_1=r_2`
B. `s_1 lt s_2` and `r_1 lt r_2`
C. `s_1 gt s_2` and `r_1 gt r_2`
D. `s_1 ne s_2 ` and `r_1 = r_2`

Answer

D

Explanation

The two data sets have the same range. The first data set has a range of 88 − 56 = 32, and the second data set has a range of 112 − 80 = 32. Alternatively, it can be seen visually that the ranges are the same because the two dot plots are aligned, the scales of the graphs are the same, and the graphs have the same width. The two data sets have different standard deviations. Both dot plots show distributions that have a mean near the center value of the dot plot. The first dot plot shows most values clustered near the mean, while the second dot plot shows most values farther from the mean. Therefore, the standard deviations of the two data sets are not equal—the data represented by the second dot plot has a greater standard deviation.
Choices A, B, and C are incorrect because they incorrectly assert either that the standard deviations are the same or that the ranges are different.