When the observations are arranged in ascending or descending order, the value which divides them into two parts is called median. Therefore median is that value below and above which 50% of observations lie. The median is not influenced by extreme values in the data whereas mean is affected by the outliers. So median is better measure than mean in case the data contains extreme values. The calculation of median for ungrouped data, grouped data and frequency distribution is slightly different.


Median of Ungrouped Data

There are two cases for calculating the median of ungrouped data. The number of observations in ungrouped data may be odd or even. The procedure for calculating the median of odd and even observations is different and is explained below.

Number of observations (odd)

If the observations are odd in numbers, then




Problem: The numbers of incorrect answers on a multiple choice test for 15 students were recorded as 3, 1, 2, 0, 4, 6, 1, 0, 1, 5, 2, 3, 3, 0, 7. Find Median.

Arrange data in ascending order
0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 6, 7




Number of observations (Even)

If the observations are Even in numbers, then median is the arithmetic mean of two central values. These two central values are calculated as:




Problem: Following are the number of miles between home and office of the 12 people who work for the same firm 1, 0, 3, 0, 3, 1, 4, 0, 5, 2, 0, 6. Calculate median.

Arrange data in ascending order:

0, 0, 0, 0, 1, 1, 2, 3, 3, 4, 5, 6




Note: The results of median will not be affected by arranging the data in ascending or descending order.


Median of grouped Data

For grouped data median is obtained by finding the size of  N/2 th value. Here N is the sum of frequencies and can be even or odd.

Problem: Find the median of the following data.






Median of Frequency Distribution

In case of frequency distribution median can be calculated with the help of following formula.



l = lower class boundary of the median class
h = Size of the median class interval
f = Frequency corresponding to the median class
N = Total number of observations i.e. sum of the frequencies.
c = Cumulative frequency preceding median class.

Problem: In a work study investigation, the times taken by 20 men, in a firm, to do a particular job were tabulated as follows: Find the median.







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