Question

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

Explanation:

• For part (a):
• The sample standard deviation measures the spread of data points around the mean. A larger number of data points that are farther from the mean will lead to a larger standard deviation.
• In data set (ii), there are more entries that are farther away from the mean compared to the other data sets.
• For the second question:
• A smaller sample standard deviation occurs when more data points are close to the mean.
• Data set (iii) has more entries that are close to the mean.

Answer:

• (a) A. Data set (ii), because it has more entries that are farther away from the mean.
• Second question: C. Data set (iii), because it has more entries that are close to the mean.