Statistical Method
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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 ‘Xbar’ 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

Add various to get

Use the formula