What is A Median in Math

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Median of a distribution is the value of the variable which divides it into two equal parts.

It is the value which exceeded by the same number of observations, i.e. it is the value such that the number of observations above it is equal to the number of observations below it. The median is thus a positional average.

In case of ungrouped data, if the number of observations is odd then the median is the value after the values has been arranged in ascending or descending order of magnitude.

Example: - The following data are the incomes (in thousands of dollars) for a sample of 11 households.
35        29        44        72        34        64        41        50        54        39        58
Find the median of this data set.

Solution: -Arrange the data in increasing order, therefore the arrange data:
29        34        35        39        41        44        50        54        58        64        72
Middle term will be the median of this data set. Hence the 6th position is the middle value.
29        34        35        39        41        44       50        54        58        64        72
Median= 44.

In case of even number of observations, there are two terms.

For example: - Find the median of the values
25        20        15        35        18        40

Solution: - Arrange data are
15        18        20       25       35        40

For this data set median will be the average of two middle term which are 3rd term and 4th term.
So Median = (20+25)/2 = 22.5