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. (b) how are the data sets the same? how do they differ? a. the three data sets have the same standard deviations but have different ranges. b. the three data sets have the same range but have different means. c. the three data sets have the same range and mean but have different standard deviations. d. the three data sets have the same mean but have different standard deviations.

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 farther 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.

Step3: Analyze data set (ii)

Data set (ii) has data points that are more spread out from the mean, which will result in a larger standard - deviation.

Step4: Analyze data set (iii)

Data set (iii) has most of its data points concentrated near the mean, so it will have the smallest standard - deviation.

Step5: Analyze range and mean

The range is the difference between the maximum and minimum values. By observing the histograms, the minimum data value is 3 and the maximum is 11 for all three data sets, so they have the same range. Also, visually, the "balance" point (approximate mean) seems to be in a similar position for all three, but the spread (standard deviation) is different.

Answer:

(a) C. Data set (ii), because it has more entries that are farther away from the mean.
B. Data set (iii), because it has more entries that are close to the mean.
(b) C. The three data sets have the same range and mean but have different standard deviations.