Question

Electing the president Refer to Exercise 91. Here are a boxplot and some numerical summaries of the electoral vote data:

(a) Explain why the median and IQR would be a better choice for summarizing the center and variability of the distribution of electoral votes than the mean and standard deviation.

(b) Identify an aspect of the distribution that the stemplot in Exercise 91 reveals that the boxplot does not.

Short answer

Part (a) The median and IOR9 are resistant, but not the mean or standard deviation.

Part (b) There is only one peak in the distribution. Instead of the three outliers represented by the boxplot, there are four more.

delivers the real values of the data

Step-by-step solution

Part (a) Step 1. Given information.

The given information is:

Part (a) Step 2. Explanation.

The median and the interquartile range (IQR) are resistant, but the mean and standard deviation aren't.

Outliers have a significant impact on the mean and standard deviation, but not on the median or IQR.

The median and the interquartile range IQR are thus better in describing the center and variability since they are not as much influenced by the outliers (as shown in the boxplot).

Part (b) Step 1. Identify an aspect of the distribution.

We can see that the distribution contains a single peak in the stemplot, which we can't see in the boxplot.

We can also see in the stemplot that there are two data values 29, implying that there are four outliers (29, 29, 38, and 55) rather than the three implied by the boxplot.

Furthermore, the stemplot displays the actual data values, which are not visible in the boxplot.