Question

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

Explanation:

Step1: Recall standard - deviation concept

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.

Step2: Analyze data set (i)

Data set (i) has a relatively symmetric and bell - shaped distribution. Most of the data is clustered around the middle values, so the data points are not too far from the mean on average.

Step3: Analyze data set (ii)

Data set (ii) has values that are concentrated at the two ends (3 and 10) with few values in the middle. These extreme values are far from the mean of the data set, which will increase the standard deviation.

Step4: Analyze data set (iii)

Data set (iii) has a more uniform distribution around the middle values. The data points are closer to the mean compared to data set (ii).

Answer:

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