# 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:

### 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.

**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

### 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

**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

Add various to get

Use the formula