Question

Select the correct answer.

The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true?
OA The mean of data set XIs greater than the mean of data set Y.
OB. The median of data set X is less than the median of data set Y.
OC. The standard deviation of data set Xis greater than the standard deviation of data set Y.
OD. The range of data set X is less than the range of data set Y.
O E.
The mode of data set X is greater than the mode of data set Y.

Answer 1

C

Explanation:

Just the spread of normally distributed data tells us nothing about the mean, mode or median, so answers A, B, and E are out of question.

The range is based on the difference between the highest and lowest elements. As there can be big outliers, we have no idea if D is true, although we expect distributions with bigger spread to generally exhibit bigger ranges.

We're left with answer C. Standard deviation is a measure of "how much the data can deviate from the mean". It's also one of the measures of spread. We expect data that's more spread out (higher spread) to have a higher standard deviation.