Statistical Method

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 Mean 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. Direct Method of Calculation of Arithmetic Mean Calculation of arithmetic mean in Simple array

(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 Indirect Method of Calculation of Arithmetic Mean Indirect method of calculation of 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 Direct Method of Arithmetic Mean in Frequency Array Direct method of arithmetic mean in Frequency array

(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 Indirect Method of Arithmetic Mean in Frequency Array Indirect method of arithmetic mean in Frequency array