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Math·Problem-Solving and Data Analysis·One-variable data: Distributions and measures of center and spread

hard

Data set A: 24, 34, 44, 54, 64

Data set A, which consists of the 5 values shown, has a mean of 44 and a standard deviation of approximately 14.10. Data set B consists of the 5 values from data set A and one additional value, $k$. For which of the following values of $k$ will the standard deviation of data set B be less than the standard deviation of data set A?

A

14

B

49

C

74

D

There is no value of $k$ such that the standard deviation of data set B will be less than the standard deviation of data set A.