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Chapter 1: Q 114. (page 78)

Birthrates in AfricaRefer to Exercise 92. Here are a boxplot and some numerical summaries of the birthrate data:

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

(b) Identify an aspect of the distribution that the dotplot in Exercise 92 reveals that the boxplot does not.

Short Answer

Expert verified

Part (a) Because they are less influenced by the skewness of the distribution, the median and interquartile range OR are better for summarising the center and variability.

Part (b) Value of actual data, Gaps, a single peak.

Step by step solution

01

Part (a) Step 1. Given information.

The given information is:

02

Part (a) Step 2. Explanation.

The median and interquartile range (IQR) are resistant, but the mean and standard deviation are not. This suggests that outliers have a large influence on the mean and standard deviation, but not on the median or the interquartile range.

The distribution is skewed to the left in the boxplot because the boxplot's box lies to the right between whiskers and the lie in the boxplot's box lies to the right of the box.

When compared to the mean and standard deviation, the median and interquartile range ICR are better at describing the center and variability since they are not as substantially influenced by the skewness of the distribution (whereas the mean and standard deviation are).

03

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

We can determine the real data values using the dot-plot since each dot represents one of the data values.

In the dot-plot, we also noticed that the distribution had a single peak, which we couldn't see in the boxplot.

Finally, we observe that the dot-plot has gaps (between certain successive data values) that are not apparent in the control chart.

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