Statistics - Arithmetic Median of Individual Series
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 −
${N}$ = 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:
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.