Statistics - Arithmetic Mean of Individual Data Series
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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 −
$X_{1}, X_{2}, X_{3}, .... X_{n}$ = 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.
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