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:

(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