Math Median

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Definition: - The Math median is the value of the middle term in a data set that has been ranked in increasing order.
It divides a ranked data set into two equal parts.

The calculation of the median consists of following steps:

·         Rank the data set in increasing order.
·         Find the middle term. The value of this term is the median.
The position of the middle term in a data set with n values is obtained as follows:

Position of the middle term= (n+1)/2

Thus we can redefine the median as follows.

Value of the median for ungrouped data

Median= value of the (n+1)/2 th term in a ranked data set.

Note:-

·         If the given data set represents a population, replace n with N.
·         If the number of observations in a data set is odd, then the median is given by the value of the middle term in the ranked data.
·         If the number of observations is even, then the median is given by the average of the values of the two middle terms.

Example:- Find the median of 10,5,19,8 and 3
Step 1: Arrange the data in increasing order
3, 5, 8, 10, 19

Step 2: There are five observation, consequently n=5 and
Position of the middle term= (n+1)/2
= (5+1)/2
= 6/2
= 3

Therefore, the median is the value of the third term in the ranked data set.
3, 5, 8, 10, 19
So Median = 8