Question

What is the impact of an outlier in the determination of an arithmetic mean?

Show by giving an example?

Answer 1

There is a drawback in the statistic of arithmetic mean as it is highly impacted by the presence of extreme values (outliers), whether large or small. 

Example:

Consider observations:  2, 5, 8, 4, 6 and 9.

Arithmetic Mean: 

x̅=1/n∑xi

Substitute values and  n=6

x̅=1/6(34)

 

x̅=5.67

Now consider same observations but with 71 as an addirional observation:  2, 5, 8, 4, 6, 9 and  71.

Arithmetic Mean: 

x̅=1/n∑xi

Substitute values and  n=7

x̅=1/7(105)

 

x̅=15

The new arithmetic mean is nearly thrice that of earlier just because of the presence of single additional large observation. 

There is a drawback in the statistic of arithmetic mean as it is highly distorted by the presence of extreme values (outliers), whether large or small.