Essential Statistics

102

Chapter 3: Measures of Variability

You should also note that outlying values in a data set will influence the

value of the range.

Example 3-3:

What is the range for the following sample values?

9, 1014, 1000, 997, 1001, 1002, 999, 995, 990

Solution:

We can arrange the data values so as to obtain the smallest and

the largest values in the data set. The ordered set is as follows:

9, 990, 995, 997, 999, 1000, 1001, 1002, 1014

Thus, the sample range =

= 1014 – 9 = 1005.

Here the value of the range is significantly affected by the outlying value of

9. This value is significantly smaller than the rest of the values in the data

set and has caused the range of the data set to be wider.

Note:

In a later chapter, we will discuss how to determine whether a data

value in a set is an outlier.

If the outlier of 9 was not in the data set, then the range

= 1014 – 990 =

24. This value of 24 is significantly smaller than 1005. Thus, one can see

the effect of an outler on the range for a set of values.

Section Review