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 Equation Equation (Here, Equation read as ‘X-bar’ and Equation 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 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.

Calculation of arithmetic mean in Simple array

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 Equation .

  • Find sum of these deviation Equation .

  • Calculate arithmetic Mean Equation

Indirect method of calculation of 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 Equation . We get Equation

  • Divide Equation by the number of observation.

  • Divide Equation by the Equation

  • Use the formula Equation

Direct method of arithmetic mean in Frequency array

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 Equation

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

  • Add various Equation to get Equation

  • Use the formula Equation

Indirect method of arithmetic mean in Frequency array

Indirect Method of Arithmetic Mean in Frequency Array

Indirect method of arithmetic mean in Frequency array

Explore NIOS Notes

Sign In