Question

Data Set A has more variation than Data Set B. Decide which of the following statements are necessarily true.

a. Data Set A has a larger mean than Data Set B.

b. Data Set A has a larger standard deviation than Data Set B.

Short answer

a. False

b. True

Step-by-step solution

Part a.

Given statement is false because mean is independent of variation of data and depends only on sum of observations.

Part b.

The given assertion is correct. The standard deviation is a measure of variance that shows how much the observations deviate from the mean on average. The standard deviation will be considered for a data collection with a lot of variances since the observations will be distant from the mean on average. The standard deviation will be minimal for a data collection with a small degree of variance since the observations will be near to the mean on average.