Chapter 10.2, Problem 14HP

To determine

To Explain: To justify the given statement

Answer to Problem 14HP

Range is always affected by outliers

Explanation of Solution

Given information:Range and outliers

Formula used:

  $\text{For}\text{Range}=\text{Highest}\text{value}-\text{Lowest}\text{value}$

Let us consider the following data

20, 30, 35, 40, 45, 50 and 250

Where 250 is an outlier

Now, the range of the data with outlier is

  $\text{Range}=250-20=230$

And the range of the data without outlier is

  $\text{Range}=50-20=30$

It can be clearly seen when outlier is considering the range is 230 while without considering the range is 30.

Hence, range is always affected by outliers.