Median of Raw Data

The median of raw data is the number which divides the observations when arranged in an order (ascending or descending) in two equal parts.


Method of finding median         

Take the following steps to find the median of raw data.

Step I: Arrange the raw data in ascending or descending order.

Step II: Let the number of variates in the data be n. Then find the following.

(i) If n is odd then \(\frac{n + 1}{2}\)th variate is the median.

(ii) If n is odd then the mean of \(\frac{n}{2}\)th and (\(\frac{n}{2}\) + 1)th variates is the median, i.e.,

median = \(\frac{1}{2}\left \{\frac{n}{2}\textrm{th Variate} + \left (\frac{n}{2} + 1\right)\textrm{th Variate}\right \}\).

Solved Example:

Find the median of the following data.

(i) 15, 18, 10, 6, 14

(ii) 8, 7, 5, 6, 3, 8, 5, 3

Solution:

(i) Arranging variates in ascending order, we get

6, 10, 14, 15, 18.

The number of variates = 5, which is odd.

Therefore, median = \(\frac{5 + 1}{2}\)th variate  

                            = 3rd variate

                            = 14.

 

(ii) Arranging variates in descending order, we get

8, 8, 7, 6, 5, 5, 3, 3.

The number of variates = 8, which is even.

Therefore, median = mean of \(\frac{8}{2}\)th and (\(\frac{8}{2}\) + 1)th variate

                            = mean of 4th and 5th variate

                            = mean of 6 and 5

                            = \(\frac{6 + 5}{2}\)

                            = 5.5

Note: The median need not be form among the variates.

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9th Grade Math

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