Question

Which one of the following statements is true?

A. The standard deviation of a data set can be larger than the mean of the data set.

B. A standard deviation will be 0 only if all values in the data set are equal to 0.

C. A sample average can never be smaller than 0.

D. The third quartile (or Q3) in a data set must always be larger than the first quartile (or

Q1) in the data set.

E. The interquartile range (or IQR) is less resistant to outliers than the standard

deviation.

Answer 1

From the given information,

We know that,

The standard deviation of a data set can be larger than the mean of the data set.

e.g., consider data set as -2,-1,0,1,2

Hence, mean=0 and standard deviation=1.58

i.e., standard deviation > Mean

Hence,

Option A. is correct.

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