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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 −
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$X_{1}, X_{2}, X_{3}, …. X_{n}$ = individual observation of variable.
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$sum {x}$ = sum of all observations of the variable
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${N}$ = 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.
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