Median

Median means the middle number.

For the given set of numbers, first we have to arrange them in order (either in ascending or descending). The middle number denotes the this.

Example 1:

Find the middle of  {3,9,5,12,7}

Solution:

I Step: Arrange them in ascending order 3,5,7,9,12

II Step: The middle value of the given 5(odd) numbers is the value of the 3rd number, that is,  7 is the answer.

Example 2:

Find the middle of {2, 13, 15, 6, 24, 9, 11, 14, 8, 21, 3, 7,17}

Solution:

I step: Arrange them in ascending order 2,3, 6, 7, 8, 9, 11, 13, 14, 15, 17,21,24.

II step: Since there are 13 (odd) numbers, the middle value is the value of the 7th number . So 11 is the answer.

Note:

In the above two examples the given Set has only odd number of values. But if we have to find the middle value of a set which has even number of values, we have to follow the step I as usual and after that in step II we have to find the average of the middle two values.

Example 3:

Find the median value of {1, 5, 7,10}

Solution:

Step I: Already the numbers are arranged in ascending order.

Step II:

  • The value of middle numbers are 5 and 7.
  • We have to find the average of 5 and 7.
  • which is (5+7)/2 = 12/2 =6
  • So the middle value is 6.

Example 4:

Find the middle value of {2, 22, 21, 12, 15, 20, 5, 14, 7, 3,1, 10, 4,11}

Solution:

Step I: Arrange them in ascending order.

           1,2,3,4,5,7,10,11,12,14,15,20,21,22.

Step II:

  • The value of the middle numbers are 10 and 11
  • Find the average of 10 and 11
  • (10+11)/2 = 21/2 = 10.5
  • So the middle value is 10.5

Note: In the above two example we have the middle values which are not given in the original set.  But half the set is below the middle value and half the set is above the middle value. So our answer is correct.

Practice problems:

  1. Find the middle value of  {200, 250, 150, 100, 350.}
  2. Find the middle value of  { 2,3,4,7,8,1,5,19, 11, 10}
  3. Find the middle value of  {11,12,13,14,15,16,19,20,21,22,23}

Solutions  

  1. 200
  2. 6
  3. 16                                          

Mode to Basic Statistics


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