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Middle/High School Algebra, Geometry, and Statistics (AGS)
9.22 Median of Discrete Values


When the observation in the data are arranged in the order (ascending or descending), the median is the middle-value. That is 50% of the observations are below the median and 50% are above it.

Following are the steps to find the median of an ungrouped frequency distribution

Step 1. Arrange the variates in the ascending order of their magnitude.
Step 2. Find the total number of variates, say n.
Step 3. If n is odd then the median is the value of [(n+1)/2]th item. If n is even then the median is the A.M. of the values of (n/2)th and [(n/2) +1]th items.

  • Find the median of the following observations

  • Solution

    i)Arranging the given data in the ascending order we get
    Here n = 11(odd)
    Median = Value of the [(11+1)/2] th item = Value of the 6th item.
    So Median = 28

    ii)Arranging the given data in the ascending order we get
    Here n = 10(even)
    Median = Value of the A.M. of (n/2)th and [(n/2)+1]th item = A.M. of the values of the 5th and the 6th items.
    So Median = (41+42)/2 = 41.5

Merits of the median
1.) It can be calculated graphically.
2.) It is not affected by extreme values.
3.) It can be determined by inspection in many cases.
Demerits of the median
1.) It is not directly based on all the values.
2.) It is not as stable as the arithmetic mean.

Q 1: The following observations have been arranged in the ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x+2, 72, 78, 84, 95.

Q 2: Numbers 50,42,41,35,2x+10,2x-8,12,11,8,6 are written in descending order and if their median is 25, find x.

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