Question

Average weight of 8 members of a group is 37. it is found that the weight of one person is wrongly marked as 63 instead of 31 find the original average of the group ?

• A. 32
• B. 33
• C. 34
• D. 55

Answer 1

Answer:

B. 33

Understanding Averages and Corrections

• The average (or mean) is calculated by dividing the sum of all values by the number of values. It's a fundamental concept in quantitative aptitude sections of competitive exams.

• When a value is incorrectly recorded, the total sum of the values is also incorrect, leading to an incorrect average. To find the original or correct average, you must first correct the total sum.

Steps to Correct the Average:

• Initial Total Weight Calculation:
  

  • Given: Number of members = 8

  • Given: Incorrect average weight = 37 kg

  • The incorrect total weight of the group = Number of members × Incorrect average = 8 × 37 = 296 kg.

• Identifying the Error:
  

  • The weight was wrongly marked as 63 kg.

  • The correct weight should have been 31 kg.

• Calculating the Correction Needed:
  

  • The difference between the wrong value and the correct value = Correct value - Wrong value = 31 - 63 = -32.

  • This means the recorded total weight was 32 kg more than it should have been.

• Adjusting the Total Weight:
  

  • To find the original (correct) total weight, subtract the excess amount from the incorrect total: 296 - 32 = 264 kg.

• Calculating the Original Average:
  

  • The original average weight = Original total weight ÷ Number of members = 264 ÷ 8 = 33 kg.