Question

Comparing SD Which of the following distributions has a smaller standard deviation? Justify your answer.

Short answer

Variable B has a smaller standard deviation.

Step-by-step solution

Step 1. Given information.

The given distributions are:

Step 2. Identify the distribution having a smaller standard deviation.

The standard deviation is a measurement of how much the data values deviate from the mean.

Because both distributions are generally symmetric, we expect the mean to be roughly in the middle of the distribution at 4.5 of the graph (for both distributions).

However, we can see that the middle bars for variable B are substantially larger than for variable A, indicating that the data values for variable B fluctuate far less from the mean.

As a result, variable B will have a lower standard deviation than variable A.