Question

The average mark in the chemistry practical exam of a class of 40 students is 100. But one student's mark was entered wrongly as 50 instead of 100. What would be the correct average?

• A. 101.25
• B. 101.20
• C. 101.35
• D. 101.21

Hint:

When correcting an average, you don't need to calculate the full sum. Just find the total error (\( \text{Correct value} - \text{Wrong value} \)) and divide it by the number of observations. Add this result to the old average if the correct value was higher, or subtract it if the correct value was lower.

Answer 1

The Correct Option is A

Step 1: Understanding the Problem
We are given an incorrect average and need to find the correct average after correcting a single data entry error.

Step 2: Key Formula or Approach
\begin{enumerate}
Calculate the incorrect total sum of marks using the formula: Sum = Average \(\times\) Number of students.
Find the difference caused by the error.
Calculate the correct total sum by adjusting the incorrect sum with the difference.
Calculate the correct average using the formula: Correct Average = Correct Sum / Number of students. \end{enumerate}
Step 3: Detailed Explanation
1. Calculate the Incorrect Sum:
Number of students = 40
Incorrect average = 100
\[ \text{Incorrect Sum} = 40 \times 100 = 4000 \] 2. Find the Error Difference:
Correct mark = 100
Wrongly entered mark = 50
\[ \text{Difference} = \text{Correct Mark} - \text{Wrong Mark} = 100 - 50 = 50 \] The sum was short by 50 marks.
3. Calculate the Correct Sum:
\[ \text{Correct Sum} = \text{Incorrect Sum} + \text{Difference} = 4000 + 50 = 4050 \] 4. Calculate the Correct Average:
\[ \text{Correct Average} = \frac{\text{Correct Sum}}{\text{Number of students}} = \frac{4050}{40} = \frac{405}{4} = 101.25 \] Alternative (Shortcut) Method:
The total sum is short by 50 marks. This shortage, when distributed among the 40 students, affects the average.
Change in average = \( \frac{\text{Total Error}}{N} = \frac{50}{40} = 1.25 \).
Since the wrong mark was smaller, the correct average will be higher.
Correct Average = Incorrect Average + Change in average = \( 100 + 1.25 = 101.25 \).

Step 4: Final Answer
The correct average mark is 101.25. Therefore, option (A) is the correct answer.