Chapter 13.3, Problem 16HP

To determine

To explain: the affect of outliers on the calculation of measures of variation in a data set.

Explanation of Solution

Measure of variation includes range and interquartile range.

1. Range is the difference between the upper and lower extreme values of the dataset.
2. Both or any one of the upper or lower extreme values of the dataset are the possible outliers.
3. Thus outliers increase the difference between the upper and lower extreme values of the dataset.
4. Therefore outlier always increases the range of the dataset.
5. Hence the range is always affected by outliers.

1. Interquartile range is difference between the third and first quartile of the dataset.
2. Thus we can say that it’s nothing but the range of the middle 50%of the dataset.
3. Therefore it depends only on the middle 50%of the dataset.
4. Hence interquartile range is not affected by the outliers.

For example consider the dataset given below,

14, 14, 14, 16, 16, 18, 18, 22, 22, 24, 24, 26, 26, 40

Here 40 is outlier,

	With outlier	Without outlier
Range	26	12
Interquartile range	9	9

Thus from the example given above, we can say that range is affected by outlier,

While interquartile range is not affected by outlier.