Question

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

Responses

{−2, −1, 0, 1, 2} because the distribution of values is symmetrical around zero.

Answer A: the set containing the following five numbers: negative 2, negative 1, 0, 1, and 2 because the distribution of values is symmetrical around zero.
A

{99.8, 99.9, 100, 100.1, 100.2} because the range of values is clustered very close to the mean.

Answer B: the set containing the following five numbers: 99.8, 99.9, 100, 100.1, and 100.2 because the range of values is clustered very close to the mean.
B

{9, 9.5, 10, 10.5, 11} because the difference between successive values is constant.

Answer C: the set containing the following five numbers: 9, 9.5, 10, 10.5, and 11 because the difference between successive values is constant.
C

{80, 93, 100, 110, 118} because the sample mean is equal to the true mean of the population.

Answer 1

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.

Step-by-step 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.