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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 |
|---|
In case of a group having even number of distribution, Arithmetic Median is found out by taking out the Arithmetic Mean of two middle values after arranging the numbers in ascending order.
Formula
Median = Value of ($frac{N+1}{2})^{th} item$.
Where −
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${N}$ = Number of observations
Example
Problem Statement −
Let”s calculate Arithmetic Median for the following individual data −
| Items | 14 | 36 | 45 | 70 | 105 | 145 |
|---|
Solution −
Based on the above mentioned formula, Arithmetic Median M will be −
$M = Value of (frac{N+1}{2})^{th} item. \[7pt]
, = Value of (frac{6+1}{2})^{th} item. \[7pt]
, = Value of 3.5^{th} item. \[7pt]
, = Value of (frac{3^{rd} item + 4^{th} item}{2})\[7pt]
, = (frac{45 + 70}{2})
, = {57.5}$
The Arithmetic Median of the given numbers is 57.5.
In case of a group having odd number of distribution, Arithmetic Median is the middle number after arranging the numbers in ascending order.
Example
Let”s calculate Arithmetic Median for the following individual data −
| Items | 14 | 36 | 45 | 70 | 105 |
|---|
Given numbers are 5, an odd number thus middle number is the Arithmetic Median.
∴ The Arithmetic Median of the given numbers is 45.
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