# Statistical Method

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### (C) Calculation of Arithmetic Mean in Frequency Distribution:

There are two methods of calculation: (i) Direct method and (ii) Indirect method

(i) Direct method:

Step:

• Take mid value of each group as the value of

• Multiply x with to obtain

• Take sum of to obtain

• Divide by to get

• Use the formula

(ii) Indirect method:

There are two versions of indirect method.

(a) Based on assumed mean

Steps:

• Take mid value (x) of each group.

• Take some value of x as assumed mean (A)

• Deduct A from x to get

• Multiply by f to get

• Take sum of all value of to obtain

• Divide by to get

• Use the formula

(a) Step Deviation Method

Steps:

• Take mid value of group X.

• Take some assumed mean (A)

• Deduct A from x to get

• Take common factor (i) from amongst value of dx.

• Divide each value of dx by this factor to get

• Multiply by f to get

• Take sum of all value of to obtain

• Use the formula

## Weighted Arithmetic Mean

Number certain weighting factors or weights depending on the significance attached to the numbers. At that time we calculate mean is called weighted mean.

Formula

## Advantages and Disadvantages of Arithmetic Mean

### Advantages:

• Easy and simple computation.

• Based on all observations of the series.

• Easily understood average.

• Treated as algebraically.

## Disadvantages:

• Not representative in case:

• Unequal classes

• Open-end classes

• Affected by extreme values in the series of extremely large and small.

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