Arithmetic Mean:

The arithmetic mean of the statistical data can be defined as quotient of sum of all the values of the variable by total number of items. It can be denoted by A.M.

For an individual series

(a)

(b)  , A is assumed mean 

For the frequency distribution,

(a) (Mean of grouped data)

(b) Short Cut Method

          , here A is assumed mean.

(c) Step Deviation Method

            , here A is assumed mean and .

Weighted Arithmetic Mean:

If w₁, w₂, w₃, ..., w_n are weights assigned to values x₁, x₂, x₃, ..., x_n respectively, then the weighted average can be defined as:

Weighted Arithmetic Mean = .

Example: A group of 10 items has the mean of 6. If mean of these4 items is 7.5, then the mean of remaining items should be

                        (A) 6.5                                                 (B) 5.5

                        (C) 4.5                                                 (D) 5.0

Solution:         Sum of all 10 items = 10 x 6 = 60

                        Sum of 4 of these items  4 x 7.5 = 30

                        ∴ sum of remaining six items = 60 -30 = 30

                        thus, the mean of remaining six items = 30/6 = 5

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