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

Explanation:

Standard deviation measures the spread of data. A greater standard deviation means data is more spread out (farther from the mean), and a smaller standard deviation means data is more clustered (closer to the mean).
For the first question:

• Data set (i) has data clustered around the mean (more entries close to the mean).
• Data set (ii) has some spread but not as much as (iii).
• Data set (iii) has more entries farther from the mean (more spread - out), so it has the greatest standard deviation.

For the second question:

• Data set (i) has more entries close to the mean. Entries close to the mean contribute less to the standard - deviation calculation (since \((x - \mu)^2\) is small when \(x\) is close to \(\mu\)). So it has the least sample standard deviation.

Answer:

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