Question

Good morning friends,
The mean and median of 100 observations are 50 and 52 .The value of the largest observation is 100 .It was later found that it is 110 not 100 . Find the true mean and median.

Answer 1

Arithmetic Mean = ∑X/N
Given : Mean = 50 and N = 100
Therefore,
50 = ∑X/100
∑X (Wrong) = 5000
Correct value = 110
Incorrect value = 100
Correct Arithmetic Mean = {∑X (Wrong) + Correct value of observation - Incorrect value of observation }/N
⇒ Correct Mean = (5000 + 110 - 100)/100
⇒ Correct mean = 5010/100
⇒ Correct Mean = 50.1
Answer
Solution no. 2 :- 
In this question, 'the value of the largest item' should be written instead of 'latest item'.
The value of the Median will not change because whatever values are added or subtracted from median, the total observation will remain 100 and median is the centrally located value of a series such that the half of the value or items of the series are above it and the other half are below it.
Formula of median = Size of (N+1)/2th Item
Total observations = 100
Size of (N+1)/2th item
⇒(100+1)/2th Item
⇒ 101/2
⇒ 50.5th Item
110 is corrected observation instead of 100 and 110 is the largest of all the observation. So it will not make any difference in value of median. The value of Median will be 52.
Answer