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Chapter 12: Problem 40

Describe why the range might not be the best measure of dispersion.

Short Answer

Expert verified
The range might not be the best measure of dispersion because it only takes into account the maximum and minimum values, omitting the spread of the remaining values. It can be significantly affected by outliers, making it less reliable than other measures of dispersion like standard deviation and interquartile range.

Step by step solution

01

Define the Range

The range is a measure of dispersion, defined as the difference between the largest and smallest values in a data set.
02

Discuss the Drawbacks of the Range

Firstly, the range only considers two values: the maximum and minimum values. Thus, it ignores how the rest of the values in the set are distributed. This can cause an inaccurate representation of dispersion, especially in sets with outliers. Additionally, the range can change significantly with addition of a single outlying value, causing instability.
03

Compare with other Measures

Compared to other measures of dispersion like standard deviation and interquartile range, the range is less reliable for indicating the spread of the majority of values, as it can be skewed by outliers.

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