In an examination, the average marks of six students were reported as 50.…
2024
In an examination, the average marks of six students were reported as 50. During cross-checking, one student’s marks were found to have been read as 48 instead of 84. Find the correct average marks of the students.
Answer: C. 56 — CONCEPTThe average of n observations is their total divided by n. If one recorded value is corrected, adjust the total by (correct value − recorded value),…
- A.
52
- B.
54
- C.
56
- D.
58
Attempted by 1 students.
Show answer & explanation
Correct answer: C
CONCEPT
The average of n observations is their total divided by n. If one recorded value is corrected, adjust the total by (correct value − recorded value), then divide by n again.
APPLICATION
The reported total is 6 × 50 = 300.
The correction to the total is 84 − 48 = 36, so the corrected total is 300 + 36 = 336.
The corrected average is 336 ÷ 6 = 56.
CROSS-CHECK
Replacing 48 with 84 increases the total by 36. Spread across six students, the average rises by 36 ÷ 6 = 6, from 50 to 56.
Therefore, the correct average marks are 56.