Individual Series Arithmetic Mean

When data is given on individual basis. Following is an example of individual series −

 Items 5 10 20 30 40 50 60 70

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

Formula

$\bar{x} = \sum_{i=1}^{n} X_{i}$

Alternatively, we can write same formula as follows −

$\bar{x} = \frac{_{\sum {x}}}{N}$

Where −

• $X_{1}, X_{2}, X_{3}, .... X_{n}$ = individual observation of variable.

• $\sum {x}$ = sum of all observations of the variable

• ${N}$ = Number of observations

Example

Problem Statement

Calculate Arithmetic Mean for the following individual data −

 Items 14 36 45 70 105

Solution

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

$\bar{x} = \frac{14 + 36 + 45 + 70 + 105}{5} \\[7pt] \, = \frac{270}{5} \\[7pt] \, = {54}$

The Arithmetic Mean of the given numbers is 54.