Question

compare the three data sets on the right. (a) which data set has the greatest sample standard deviation? a. data set (iii), because it has more entries that are farther away from the mean. b. data set (ii), because its data have more variability. c. data set (i), because it contains the greater number of entries.

Explanation:

Standard deviation measures the spread or variability of data. A data set with more entries far from the mean has a larger standard deviation. Looking at the histograms:

• Data set (i) has data clustered closely around the mean (it is more symmetric and the bars are concentrated in the middle).
• Data set (ii) has some spread but not as much as (iii).
• Data set (iii) has data values that are more spread out from the center (more entries far from the "middle" of the data range).

Answer:

A. Data set (iii), because it has more entries that are farther away from the mean.