Question

compare (i) the three data sets on the right. (a) which data set has the greatest sample standard deviation? a. data set (ii), because it has more entries that are close to the mean. b. data set (iii), because it has two entries that are far away from the mean. c. data set (i), because it has more entries that are farther away from the mean. which data set has the least sample standard deviation? a. data set (iii), because it has less entries that are farther away from the mean. b. data set (ii), because it has more entries that are close to the mean. c. data set (i), because it has more entries that are farther away from the mean.

Explanation:

Step1: Recall standard - deviation concept

The sample standard deviation measures the amount of variation or dispersion of a set of values. A larger standard deviation indicates that the data points are more spread out from the mean, and a smaller standard deviation indicates that the data points are closer to the mean.

Step2: Analyze first question

For the data - set with the greatest sample standard deviation, we look for the data - set with more data points far from the mean. Data set (i) has more entries that are farther away from the mean compared to (ii) and (iii), so it has the greatest standard deviation.

Step3: Analyze second question

For the data - set with the least sample standard deviation, we look for the data - set with more data points close to the mean. Data set (ii) has more entries that are close to the mean compared to (i) and (iii), so it has the least standard deviation.

Answer:

First question: C. Data set (i), because it has more entries that are farther away from the mean.
Second question: B. Data set (ii), because it has more entries that are close to the mean.