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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: Observe the number of variates in the data. Let the number of variates in the data be n. Then find the median as following.

(i) If n is odd then n+12th variate is the median.

(ii) If n is even then the mean of n2th and (n2 + 1)th variates is the median, i.e.,

median = 12{n2th Variate+(n2+1)th Variate}.

Solved Examples on Median of Raw Data or Median of Ungrouped Data:

1. Find the median of the ungrouped data.

15, 18, 10, 6, 14

Solution:

Arranging variates in ascending order, we get

6, 10, 14, 15, 18.

The number of variates = 5, which is odd.

Therefore, median = 5+12th variate  

                            = 3rd variate

                            = 14.


2. Find the median of the raw data.

8, 7, 15, 12, 10, 8, 9

Solution:

Arranging the variates in ascending order, we get

7, 8, 8, 9, 10, 12, 15.

The number of variates = 7, which is odd.

Therefore, median = the 7+12th variate  

                            = 4th variate

                            = 9.


3. Find the median of the ungrouped data.

10, 17, 16, 21, 13, 18, 12, 10.

Solution:

Arranging the variates in ascending order, we get

10, 17, 16, 21, 13, 18, 12, 10.

The number of variates = 8, which is even.

Therefore, median = mean of the 82th and (82 + 1)th variate

                            = mean of the 4th and 5th variates

                            = mean of 13 and 16

                            = (13+162

                            = (292

                            = 14.5.

Median of Raw Data

4. Find the median of the raw data.

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

Solution:

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 82th and (82 + 1)th variate

                            = mean of 4th and 5th variate

                            = mean of 6 and 5

                            = 6+52

                            = 5.5

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





9th Grade Math

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