What is the impact of an outlier in the determination of an arithmetic mean? Show by giving an example?

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

Show by giving an example?

Expert Solution

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.

Shams answered 2 years ago

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