Economics » Methods and Tools of Economic Analysis » Measures Of Central Tendency

# Arithmetic Mean

## Measures of Central Tendency

Measures of central tendency, also called measures of location, are the statistical information that give the middle or average of a set of data. They are:

## Arithmetic Mean

This is also referred to as mean. It is the average of a series of values or figures. It is obtained by dividing the sum of these figures by the total number of the values or figures.

$$\bar{x} = \cfrac{\sum x}{n}$$

where $$\bar{x} =$$ Arithmetic mean,
$$\sum =$$ sum of, and
$$n =$$ number of figures

### Example:

Calculate the mean of the following series: 14, 18, 24, 16, 30, 12, 20, and 10.

Solution:

$$\bar{x} = \cfrac{\sum x}{n}$$

$$\bar{x} = \cfrac{144}{8}$$

$$\bar{x} = 18$$

### Merits of the Mean

1. It is easy to calculate.
2. It gives an exact value.
3. It makes use of all available information in a set of data.
4. It provides a good method of comparing values.

### Demerits of the Mean

1. Arithmetic mean cannot be obtained graphically.
2. It may be difficult to obtain without calculation.
3. It may be badly affected by extreme values (the minimum and maximum values in a data set) in a distribution.

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