Which of the following data sets has the smallest standard deviation and provides correct reasoning as to why it has the smallest standard deviation?

A. \{-2, -1, 0, 1, 2\} because the distribution of values is symmetrical around zero.
B. \{99.8, 99.9, 100, 100.1, 100.2\} because the range of values is clustered very close to the mean.
C. \{9, 9.5, 10, 10.5, 11\} because the difference between successive values is constant.
D. \{80, 93, 100, 110, 118\} because the sample mean is equal to the true mean of the population.

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Qwship Qwship · Answer 2 · 2025-04-22T01:12:09-04:00

Final answer:

The data set {99.8, 99.9, 100, 100.1, 100.2} has the smallest standard deviation because all its values are clustered very closely to the mean, resulting in smaller distances from the mean and less dispersion.

Explanation:

Out of the given data sets, option B {99.8, 99.9, 100, 100.1, 100.2} has the smallest standard deviation. The standard deviation measures the average distance of each data point from the mean. In option B, all the values are very closely clustered around the mean, meaning the distances from the mean are quite small. This results in a smaller standard deviation. The reasoning behind this is that the closer the data points are to the mean, the less dispersion or variability they present, thus resulting in a smaller standard deviation. The other data sets present with higher variability, especially A and D, causing their standard deviations to be higher.

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