”;
When data is given along with their frequencies. Following is an example of discrete series −
| Items | 5 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
|---|---|---|---|---|---|---|---|---|
| Frequency | 2 | 5 | 1 | 3 | 12 | 0 | 5 | 7 |
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 discrete data −
| Items, ${X}$ | 14 | 36 | 45 | 70 | 105 | 145 |
|---|---|---|---|---|---|---|
| Frequency, ${f}$ | 2 | 5 | 2 | 3 | 12 | 4 |
| Comulative Frequency, ${C_f}$ | 2 | 7 | 9 | 12 | 24 | 28 |
| Terms | 1-2 | 3-7 | 8-9 | 10-12 | 13-24 | 25-28 |
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{28+1}{2})^{th} item. \[7pt]
, = Value of 14.5^{th} item. \[7pt]
, = Value of (frac{14^{th} item + 15^{th} item}{2})\[7pt]
, = (frac{105 + 105}{2})
, = {105}$
The Arithmetic Median of the given numbers is 2.
In case of a group having even 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 discrete data −
| Items, ${X}$ | 14 | 36 | 45 | 70 | 105 |
|---|---|---|---|---|---|
| Frequency, ${f}$ | 2 | 5 | 1 | 4 | 13 |
| Comulative Frequency, ${C_f}$ | 2 | 7 | 8 | 12 | 25 |
| Terms | 1-2 | 3-7 | 8-8 | 9-12 | 13-25 |
Given numbers are 25, an odd number thus middle number, 12th term is the Arithmetic Median.
∴ The Arithmetic Median of the given numbers is 70.
Calculator
”;