Mean

Mean is the arithmetic average.

To find mean of ungrouped data

It is obtained by adding the raw scores and dividing the sum by the number of items.

Suppose the raw scores are

x₁, x₂, x₃,…, x_N

then, mean

where M = mean

x = each score or item

N = number of items

= sigma, which means 'summation of '

Find the mean of 6, 10, 4, 12, 8.

M = 8

The weight in kg of the 9 members of a school tug-of-war team are: 54, 59, 63, 53, 73, 49, 50, x, 45.

If the average weight is 56 kg, find x.

x = 58.

To find mean for grouped data

There are three methods to find mean for a frequency distribution.

(i) Direct method:

where x is the mid-interval

f is the frequency

M is the mean

(ii) Short-cut method:

where A = assumed mean

d = x - A

(iii) Step-deviation method:

where i = class size

We illustrate each of these methods with the help of the following examples.

Find the mean for the following table by the 'Direct Method'

Calculate the mean marks in the distribution below by the 'Direct Method'.

Direct Method:

= 29.75

Calculate the mean of the question in example 4 by Short-Cut Method.

Short-cut Method:

(i) This method makes the calculations easy.

(ii) We assume mean as A, one of the class-marks near the middle of the 'x' column.

(iii) Then, an additional column d = x - A is formed.

(iv) The mean is calculated by applying the formula.

Assumed mean = A = 24.5

M =

= 24.5 + 5.25

= 29.75

The answer remains the same by any method.

Weights of 50 eggs were recorded as given below. Calculate their mean weight to the nearest gram by Step Deviation Method:

Step - Deviation Method:

Assumed mean = A = 97.5

M =

= 97.5 - 1.6

= 95.9

= 96 gm

Once you have mastered this method, statistical calculations become very easy. Large values of x are reduced to single digit numbers by Step-Deviation Method.