Statistical Method
(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

Openend classes


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