MEASURES OF CENTRAL TENDENCY BCOM 1ST YEAR
QUESTION: “Median is not affected by extreme values unlike arithmetic mean.” Discuss.
It is true than Median does not get affected by the extreme values but mean gets affected by the extreme values. This is because in case of mean the values of the items are considered but in case of median only the numbers of values are taken into consideration and not the values.
Example: Suppose X= 1, 2, 4, 6, 8, 9, 10
Mean = (1+2+4+6+8+9+10)/ 7= 40/7= 5.714
Median = (N+1)/2= (7+1)/2= 4th item = 6
Now, lets introduce an extreme item in the given series
X= 1,2,3,4,6,8,9, 10,42
Now Mean is= (1+2+3+4+6+8+9+10+42)/9= 85/9= 9.44
Now Median is= (9+1)/2= 5th item= 6
When the extreme items are introduced, the mean becomes 9.44 directly from 5.714 but the median remains same i.e. 6. This shows that Median is not affected by the extreme values.