The average of 50 numbers is 38. If two numbers namely 45 and 55 are…
2014
The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, the average of rest 48 numbers is
- A.
36.5
- B.
37
- C.
37.5
- D.
38
Show answer & explanation
Correct answer: C
Concept: The average of a set of numbers is the sum of all the numbers divided by how many numbers there are. When some numbers are removed from the set, the new average of the remaining numbers equals (original sum minus the sum of the removed numbers) divided by the new count.
Application:
Original sum of the 50 numbers = average × count = 50 × 38 = 1900.
Sum of the two discarded numbers = 45 + 55 = 100.
Sum of the remaining 48 numbers = original sum − discarded sum = 1900 − 100 = 1800.
New average of the remaining 48 numbers = remaining sum ÷ remaining count = 1800 ÷ 48 = 37.5.
Cross-check: 48 × 37.5 = 1800. Adding the discarded sum back gives 1800 + 100 = 1900, and 1900 ÷ 50 = 38, which matches the original average given in the question — confirming the working is consistent.
So the average of the remaining 48 numbers is 37.5.