Which of the following data sets has the smallest standard deviation, and what is 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.

Question

31-12-2024
Mathematics

College

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Which of the following data sets has the smallest standard deviation, and what is 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 :

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RoseDavidson RoseDavidson · Answer 1 · 2024-07-10T16:22:09-04:00

Final answer:

The data set {99.8, 99.9, 100, 100.1, 100.2} has the smallest standard deviation because the range of values is clustered very close to the mean.

Explanation:

The data set {99.8, 99.9, 100, 100.1, 100.2} has the smallest standard deviation because the range of values is clustered very close to the mean.

The standard deviation measures the spread of data around the mean, so when the data values are tightly clustered around the mean, the standard deviation is smaller.

In this case, the range of values is very close to the mean, indicating less variation and a smaller standard deviation.