the average marks in science subject of a class of 20 students is 68. if the marks of two students were misread as 48 and 65 instead of the actual marks 72 and 61 respectively, what would be the correct average?
Here’s a clear, detailed, and friendly-professional styled explanation of the problem.
The Average Marks Correction Problem
Quick Scoop
A common exam mistake — marks recorded incorrectly — can change the class average. Let’s fix it step-by-step.
📊 Given Information
- Number of students = 20
- Reported average marks = 68
- Misread marks: 48 and 65
- Actual marks: 72 and 61
🧮 Step-by-Step Calculation
- Find the total marks based on reported data:
Total (wrong)=20×68=1360\text{Total (wrong)}=20\times 68=1360Total (wrong)=20×68=1360
- Find out how much the misread values differ:
(Actual marks total)−(Misread marks total)=(72+61)−(48+65)(\text{Actual marks total})-(\text{Misread marks total})=(72+61)-(48+65)(Actual marks total)−(Misread marks total)=(72+61)−(48+65)
=133−113=+20=133-113=+20=133−113=+20
So, the correct total marks should be 20 more than 1360.
- Compute the corrected total marks:
Total (correct)=1360+20=1380\text{Total (correct)}=1360+20=1380Total (correct)=1360+20=1380
- Now, find the correct average:
Correct average=138020=69\text{Correct average}=\frac{1380}{20}=69Correct average=201380=69
✅ Final Answer
The correct average marks of the class are 69.
Table Summary
| Detail | Value |
|---|---|
| Total students | 20 |
| Wrong average | 68 |
| Wrong total marks | 1360 |
| Adjustment (due to misread marks) | +20 |
| Correct total marks | 1380 |
| Correct average | 69 |
