# Discrete Series Arithmetic Mean

When data is given along with their frequencies. Following is an example of discrete series −

 Items Frequency 5 10 20 30 40 50 60 70 2 5 1 3 12 0 5 7

For discrete series, the Arithmetic Mean can be calculated using the following formula.

## Formula

$\bar{x} = \frac{f_1x_1 + f_2x_2 + f_3x_3........+ f_nx_n}{N}$

Alternatively, we can write same formula as follows −

$\bar{x} = \frac{\sum fx}{\sum f}$

Where −

• ${N}$ = Number of observations

• ${f_1,f_2,f_3,...,f_n}$ = Different values of frequency f.

• ${x_1,x_2,x_3,...,x_n}$ = Different values of variable x.

## Example

Problem Statement

Calculate Arithmetic Mean for the following discrete data −

 Items Frequency 14 36 45 70 2 5 1 3

Solution

Based on the given data, we have −

Items Frequency
f
${fx}$
14 2 28
36 5 180
45 1 45
70 3 210
${N=11}$ ${\sum fx=463}$

Based on the above mentioned formula, Arithmetic Mean $\bar{x}$ will be −

$\bar{x} = \frac{463}{11} \\[7pt] \, = {42.09}$

The Arithmetic Mean of the given numbers is 42.09.