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 ‘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 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 .

  • Find sum of these deviation .

  • Calculate arithmetic Mean

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 . 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

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

Indirect method of arithmetic mean in Frequency array