Statistics - Inspanidual Series Arithmetic Median

When data is given on inspanidual basis. Following is an example of inspanidual 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 inspanidual 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 inspanidual 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.

Statistics - Inspanidual Series Arithmetic Median

Formula

Example

Example

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