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 data dispersion from the mean. More spread - out data has a higher standard deviation.

Step2: Analyze data set (i)

Data set (i) has a somewhat symmetric distribution around the mean, with most data close to the mean.

Step3: Analyze data set (ii)

Data set (ii) has data points that are more spread out from the mean compared to (i) and (iii), so it has the greatest standard deviation.

Step4: Analyze data set (iii)

Data set (iii) has most of its data points clustered closely around the mean, so it has the least standard deviation.

Step5: Analyze range and mean

The range is the difference between the maximum and minimum values. By observing the histograms, all three data sets have the same minimum (3) and maximum (11), so they have the same range. Also, visually, the "center" of the distributions seems to be around the same value, indicating they have the same mean. But their standard deviations are different.

Answer:

(a) Which data set has the greatest sample standard deviation? 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? 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.