Question

which of the following statements must be true about the data sets a and b displayed in the histograms above? a the mean of data set a is equal to the mean of data set b. b the median of data set a is equal to the median of data set b. c the range of data set a is equal to the range of data set b. d the standard deviation of data set a is less than the standard deviation of data set b. e the standard deviation of data set a is greater than the standard deviation of data set b.

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum.

Step2: Find range for Data Set A

In Data Set A, minimum is 10 and maximum is 60. So range of A is $60 - 10=50$.

Step3: Find range for Data Set B

In Data Set B, minimum is 10 and maximum is 60. So range of B is $60 - 10 = 50$.

Step4: Compare ranges

Since range of A and B are both 50, the ranges are equal.

Answer:

C. The range of data set A is equal to the range of data set B.