# Statistical Method

## Arithmetic Mean Equation

• 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:

### (A) Calculation of arithmetic mean in Simple array:

There are two methods of calculation: (i) Direct method and (ii) Indirect method

(i) Direct method: Marks obtained by 5 students in the subject of statistics.

(ii) 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

### (B) Calculation of arithmetic mean in Frequency array:

There are two methods of calculation: (i) Direct method and (ii) Indirect method

(i) 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 observation.

• Divide by the

• Use the formula

(ii) 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