Failure of Arithmetic Mean as Central Tendency

In this class, We discuss Failure of Arithmetic Mean as Central Tendency.

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The reader should have prior knowledge of Arithmetic mean. Click Here.

First, We understand the situations where the arithmetic means is suitable.

Example:

Arithmetic mean works well if there is an additive relationship between numbers.

1, 4, 7, 10, 13, 16, 19

We obtain each number by the addition of 3 with the previous number.

X’ = Mean = (1+4+7+10+13+16+19)/7

X’ = 10

The mean works well as a measure of central tendency.

Failure of measure of central tendency example

Arithmetic mean fails if the data have multiplicative or exponential relation.

Example:

1, 3, 9, 27, 81, 243, 729

X’ = Mean = (1 + 3 + 9 + 27 + 81 + 243 + 729)/7

X’ = 156.1

The mean value is not near to the measure of central tendency.

The mean value is moving towards a large number.

The large values impact much in moving mean value towards them. Because we do addition in mean.

Failure of arithmetic means a central tendency with outliers

Example:

Employee salaries: 30, 32, 35, 45, 38, 42, 43, 250

all the employee’s salaries are around 35 – 45k.

One employee’s salary is around 250K. He is the CEO of the company.

The CEO’s salary is considered an outlier.

The value is away from most of the data values.

X’ = Mean = 64.375.

Because of outlier data, the mean value moves away from the measure of central tendency.

Failure of arithmetic means with different units

Example:

5.5, 5.6, 5.8, 6, 145, 153, 180, 182

Few values are in feet and inches.

Few values are in centimetres.

Centimetres are giving more impact to move the mean value towards 180.

All values should be in the same units.