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.

Explanation:

Standard deviation measures the spread of data. Data points farther from the mean increase the standard deviation. In dataset (i), there are two data points that are far from the central cluster (the mean - like the ones at the bottom of the plot). Dataset (ii) has data points more clustered around the center (so less spread), and dataset (iii) also has data points more evenly distributed around the center with no extreme outliers like in dataset (i).

Answer:

B. Data set (i), because it has two entries that are far away from the mean.