Question

Why is RANGE a bad measure of dispersion in real life statistics?

Answer 1

The RANGE is a bad measure of dispersion because it is affected by outliers.It only uses the two extreme values in a dataset.

Explanation:

The range is given by the formula:

$$\text{Range} =  \text{Maximum} - \text{Minimum} $$

By using the two extreme values in a dataset, it is quite wasteful of resources because all the values in between the maximum and minimu are neglected. The insight they can contribute in determining the shape of the data is not harnessed.

Being extreme values they are prone to manipulation by outliers as shown in the example below.

Example:

Given the marks of an exam out $100$, which class did better? $A$ or $B$?

$$A = \{3,3,3,3,3,3,3,3,3,100\}$$

$$B = \{3,3,3,3,3,3,3,3,3,3\}$$

The arithmetic mean for class $A$ is $12.7$, Median = Mode = $3$ and Range = $97$

The arithmetic mean for class $B$ is $3$, Median = Mode = $3$ and Range = $0$

You can see that it appears as though class $A$ did much better than class $B$ and if we are to report on the measures of dispersion it can be seen that the range for $A$ was big implies huge volatility in the class' marks, which is not true. Only one learner, an outlier badly affected the mean and range of the class. This learner who got $100$ increased both statistics thus we cannot extract the true story because the RANGE has been a victime of outliers.