How to Calculate Arithmetic Mean (A.M) in discrete Series?

Discrete series means where frequencies of a variable are given but the variable is without class intervals.

Here the mean can be found by Three Methods.

(i) Direct Method:

Here each frequency is multiplied by the variable, taking the total and dividing total by total number of frequencies, we get X.

Symbolically,

X = ∑fx/N

Where f = frequency,

X = the value of the variable

And N = the sum of frequency or N = ∑f

Example 1. Calculate A.M. from the following data

Solution:

(ii) Short Cut Method:

Here Assumed Mean is taken and taking deviations of variable from it. We obtain X by using the following formula.

Where A = Assumed Mean

dx = (X-A);

f = frequency ∑f or N = Total number of terms,

(Note :-This formula is often used when the variables are large in size or infractions and direct formula is not easy to use.)

Example 2. Calculate the Arithmentic Mean using short-cut method:

Solution:

Important:

But this formula cannot be applied to every data. For example if in the given example, values of X are 4, 7, 12, 17, 19 ; the common factor cannot be procured in this case. Hence problem in such a case will be solved by Direct or Short Cut method.