The mean of 50 numbers is 30. Later it was discovered that two entries were wrongly entered as 82 and 13 instead of 28 and 31. Find the correct mean.

A. 36.12

B. 30.66

C. 29.28

D. 38.21

Answer: Option C

Solution(By Examveda Team)

According to the question,
The mean of 50 numbers is = 30
Sum of 50 numbers is = 50 × 30 = 1500
Later it was discovered that two entries were wrongly entered as 82 and 13 instead of 28 and 31.
∴ Difference = (82 + 13) - (28 + 31)
= 95 - 59
= 36 (extra)
∴ Actual sum of 50 numbers is = 1500 - 36 = 1464
∴ Actual average = $$\frac{1464}{50}$$   = 29.28