Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true?
A) The locations of the distributions are different.
B) The distributions are from two different families.
C) The dispersions of the distributions are different.
D) The dispersions of the distributions are the same.

Question

Quizplus · Accepted Answer

The given normal distributions have the same mean but different standard deviations. The standard deviation is a measure of dispersion, indicating how much the data varies from the mean. Thus, we can conclude that the dispersions of the distributions differ, making choice C the correct answer. Choice A is not correct because the locations of the distributions are the same (at a mean of 10), not different. Choice B is also not correct because both distributions are normal distributions, so they belong to the same family of distributions. Choice D is not correct because the standard deviations (which measure dispersion) are different.

Two Normal Distributions Are Compared