Question

Comparing SD The parallel dotplots show the lengths (in millimeters) of a sample of 11 nails produced by each of two machines. Which distribution has the larger standard deviation? Justify your answer.

Short answer

Machine A has a larger standard deviation.

Step-by-step solution

Step 1. Given information.

The given dot plots are:

Step 2. Identify the dot-plot having a larger standard deviation.

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

As we can observe that both distributions are symmetric (a section of the graph is the mirror image of the other part of the graph), we expect the mean to be nearly in the middle of the distribution at 70 of the graph (for both distributions).

However, we notice that machine A has more dots in the middle at 70 than machine B, indicating that machine A's data values fluctuate significantly less from the mean than machine B's.

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