Statistical Method

Download PDF of This Page (Size: 298K)

(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

Direct method of arithmetic mean in Frequency distribution

Direct Method of Arithmetic Mean in Frequency Distribution

Direct method of arithmetic mean in Frequency distribution

(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

Indirect method based on assumed mean in Frequency distribution

Indirect Method Based on Assumed Mean in Frequency Distribution

Indirect method based on assumed mean in Frequency distribution

(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

Indirect method step deviation Method in frequency distribution

Indirect Method Step Deviation Method in Frequency Distribution

Indirect method step deviation Method in frequency distribution

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.