Question

The average mark of 40 students in the class 8 mathematics test was 70. It was later found that the marks of two students had been wrongly entered as 47 instead of 74 and 46 instead of 64. What is the correct average?

• A. 71.125
• B. 71.215
• C. 70.125
• D. 70.215

Answer 1

Answer:

A. 71.125

Understanding the Concept of Average

• The average (or mean) is calculated by summing all the values in a dataset and dividing by the number of values.

• Formula: Average = (Sum of all observations) / (Number of observations)

Initial Calculation Breakdown

Given Information:

• Number of students (observations) = 40

• Initial average mark = 70

Calculating the Initial Sum of Marks:

• Initial Sum = Initial Average × Number of students

• Initial Sum = 70 × 40 = 2800

Identifying and Correcting Errors

Details of the Wrongly Entered Marks:

• Student 1: Entered as 47, Correct mark was 74.

• Student 2: Entered as 46, Correct mark was 64.

Calculating the Difference in Marks:

• Difference for Student 1 = Correct Mark - Entered Mark = 74 - 47 = +27

• Difference for Student 2 = Correct Mark - Entered Mark = 64 - 46 = +18

• Total increase in sum = 27 + 18 = 45

Calculating the Correct Sum and Average

Correcting the Total Sum of Marks:

• Correct Sum = Initial Sum + Total Increase in Sum

• Correct Sum = 2800 + 45 = 2845

Calculating the Correct Average:

• Correct Average = Correct Sum / Number of students

• Correct Average = 2845 / 40

• Correct Average = 71.125