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

Explanation:

• For (a):
• The standard deviation measures the spread of data. Data set (iii) has more entries far from the mean, so it has the greatest standard deviation. Data set (i) has more entries close to the mean, so it has the least standard deviation.
• For (b):
• Looking at the histograms, the range (difference between maximum and minimum data values) and mean (central tendency) can be visually compared. The three data - sets have the same range (from 3 to 11) and mean (around the central value of the x - axis range), but different spreads (standard deviations).

Answer:

(a)

• Greatest sample standard deviation: A. Data set (iii), because it has more entries that are farther away from the mean.
• Least sample standard deviation: C. Data set (i), because it has more entries that are close to the mean.

(b) A. The three data sets have the same range and mean but have different standard deviations.