# Statistical Methods: Arithmetic Mean and Calculation of Arithmetic Mean

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## Arithmetic Mean (X [Bar])

• In statistics average is termed as the arithmetic mean.

• It is calculated by taking all items of series into account.

• Mean (Here, read as ‘X-bar’ and as ‘sigma x’)

## Calculation of Arithmetic Mean

• Method of presentation of data is different in each case.

• Calculation of arithmetic mean in following methods of presentation: Methods of Presentation of Arithmetic MeanCalculation of arithmetic mean in following methods of presentation

### Calculation of Arithmetic Mean in Simple Array

There are two methods of calculation:

(i) Direct method and

(ii) Indirect method

Direct method

Marks obtained by 5 students in the subject of statistics. Direct Method of Calculation of Arithmetic MeanCalculation of arithmetic mean in Simple array

Indirect method

Steps:

• Take some observation as assumed mean. For ex. here, we assumed 20 mean.

• Find deviation (dx) of each observation.

• Find sum of these deviation.

• Calculate arithmetic Mean Indirect Method of Calculation of Arithmetic MeanIndirect method of calculation of arithmetic mean

### Calculation of Arithmetic Mean in Frequency Array

There are two methods of calculation:

(i) Direct method and

(ii) Indirect method

Direct method

Steps:

• Multiply each value of X by its frequency (f).

• Take sum of all values of . We get

• Divide by the number of observations.

• Divide by the

• Use the formula Direct Method of Arithmetic Mean in Frequency ArrayDirect method of arithmetic mean in Frequency array

Indirect method

Steps:

• Select a suitable assumed average (A).

• Find deviations of each observation from A to get

• Multiply each by its respective frequency (f) to get