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.
which data set has the least sample standard deviation?
a. data set (ii), because it has no entries near the mean.
b. data set (iii), because it has more entries that are close to the mean.
c. data set (i) because it has more entries near the mean than far away from it.

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures the amount of variation or dispersion of a set of values. A larger standard deviation means more data points are far from the mean, and a smaller standard deviation means more data points are close to the mean.

Step2: Analyze data set (i)

Data set (i) has a relatively symmetric distribution with most data points clustered around the middle values. There are not many data points that are extremely far from the mean.

Step3: Analyze data set (ii)

Data set (ii) has two peaks at the two - ends of the data range. There are a significant number of data points that are far from the mean. So, it has a large standard deviation.

Step4: Analyze data set (iii)

Data set (iii) has most of its data points clustered around a single value. Most data points are close to the mean, so it has a small standard deviation.

Answer:

(a) C. Data set (ii), because it has more entries that are farther away from the mean.
(b) B. Data set (iii), because it has more entries that are close to the mean.