Median definition statistics| Median formula | How to find the Median.

Median definition statistics :
if the set contains an odd number of items, the middle item of an array is median. in array we arrange the data in ascending or descending order of magnitude.
Median is a positional average. it indicates the value of the item positioned at the center. it is 50th percentile. the value below and above median is 50%.

           Mean      Mode        Quartile

How to find Median :
Median formula :
If data set contains an odd number of items then,
Me = value of [ ( n + 1 ) / 2 ] th item.
here, n = total frequency of distribution.

If data set contains an even number of items then, there will be two items which stand at the center. therefore,
Me = we may take the average of these two, as the median.

Median based on Individual Data :
Que. 1 : Calculate median for the following data.
24, 36, 9, 26, 78, 46, 4.
Ans. :
First we, Arrange the data in ascending order
4, 9, 24, 26, 36, 46, 78.
here, n = 7
Me = Size of [ ( n + 1 ) / 2 ] th item
      = Size of ( 7 + 1 ) / 2 th item
      = Size of 4th item
Me = 26

Que. 2 : Calculate median for the following data.
40, 57, 11, 4, 6, 79, 90, 31, 50.
Ans. :
First we, Arrange the data in ascending order
4, 6, 11, 31, 40, 50, 57, 79, 90.
here, n = 9
Me = Size of [ ( n + 1 ) / 2 ] th item
      = Size of ( 9 + 1 ) / 2 th item
      = Size of 5th item
Me = 40

Que. 3) Compute Median for the following data
50, 32, 78, 46, 65, 22.
Ans. : First we, Arranging the data in ascending order
22, 32, 46, 50, 65, 78.
here, n = 6
there will be two items which stand at the center. therefore,
The middle values are 3rd and 4th which assumes values as 46 and 50.
Now, Me = ( 46 + 50 ) / 2
Me = 96 / 2
therefore, Me = 48.

Que. 4) Compute Median for the following data
5, 1, 8, 14, 3, 10, 16, 20.
Ans. : First we, Arranging the data in ascending order
1, 3, 5, 8, 10, 14, 16, 20.
here, n = 8
there will be two items which stand at the center. therefore,
The middle values are 4th and 5th which assumes values as 8 and 10.
Now, Me = ( 8 + 10 ) / 2
Me = 18 / 2
therefore, Me = 9.





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