If distribution A and distribution B have the same mean but A has a larger standard deviation, we may conclude that________.
A) the medians of both distributions would be the same.
B) distribution B has a range of 0.
C) A has a greater degree of variation.
D) distribution B displays more variety.

Question

Quizplus · Accepted Answer

Standard deviation is a measure of variation in data. A larger standard deviation means there is more spread in the data, indicating a greater degree of variation. The mean and median can be the same in both distributions, but the larger standard deviation in distribution A implies more variability. Option B cannot be true because a zero range would mean all the values in distribution B are the same which may not be the case when only the mean is the same as that of distribution A. Option D is not a valid statistical concept.

If Distribution a and Distribution B Have the Same Mean