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Which of the following data sets has the smallest standard deviation, and which option provides the correct reasoning for 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.

Answer :

Final answer:

Option B, {99.8, 99.9, 100, 100.1, 100.2} has the smallest standard deviation due to the values being clustered close to the mean.


Explanation:

The correct answer is option B. {99.8, 99.9, 100, 100.1, 100.2} because the range of values is clustered very close to the mean. The standard deviation measures how spread out the data points are from the mean. In this data set, the values are very close to each other and to the mean, resulting in a small standard deviation.


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