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Chapter 1: Q76SE (page 49)

The three measures of center introduced in this chapter are the mean, median, and trimmed mean. Two additional measures of center that are occasionally used are the midrange,which is the average of the smallest and largest observations, and the midfourth,which is the average of the two fourths. Which of these five measures of center are resistant to the effects of outliers and which are not? Explain your reasoning.

Short Answer

Expert verified

Mean and midrange is not resistant to the outliers.

Median, trimmed mean and mid-fourth are resistant to the outliers.

Step by step solution

01

Given information

The three measures of center are mean, median, and trimmed mean.

The two additional measures of the center that are used are midrange and mid-fourth.

02

Explain which measure of center is resistant to the effects of outliers

From the provided measures of center, mean, and midrange are computed by using the extreme values. This implies that they are not resistant to the outliers.

Median, trimmed mean and mid-fourth takes the position of values into account and the values themselves. This implies that they are most resistant to the outliers.

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5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3

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5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6

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8.3 3.2 4.9 5.0 6.0 8.2 6.3 3.8 6.0

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