Question

Average weight of 10 students of a class is 40 if weight of one student marked as 80 instead of 60. Find the original average of students weight

• A. 38
• B. 42
• C. 40
• D. 50

Answer 1

Answer:

A. 38

Understanding Average Correction

• The average (or mean) is calculated by dividing the sum of all quantities by the number of quantities. Formula: Average = Sum / Count.

• In problems where an incorrect value is recorded, the primary step is to find the error in the total sum.

• Initially, the total weight of the 10 students was calculated using the given (incorrect) average.

  • Number of students (Count) = 10

  • Reported Average = 40 kg

  • Reported Total Weight = Count × Reported Average = 10 × 40 = 400 kg.

• An error occurred in recording one student's weight: it was marked as 80 kg instead of the correct 60 kg.

• This means an excess weight was added to the total. To find this excess:

  • Excess Weight = Incorrect Weight - Correct Weight = 80 kg - 60 kg = 20 kg.

• To find the correct total weight, subtract the excess weight from the reported total weight.

  • Correct Total Weight = Reported Total Weight - Excess Weight = 400 kg - 20 kg = 380 kg.

• Finally, calculate the original (correct) average by dividing the correct total weight by the number of students.

  • Original Average = Correct Total Weight / Count = 380 kg / 10 = 38 kg.