Question

The mean of 9 numbers is 50. One of the numbers is wrongly recorded as 63 instead of 36. What is the correct mean?

• A. 47
• B. 48
• C. 49
• D. 50

Hint:

Corrected mean = Wrong total − Wrong value + Correct value, then divide by count.

Answer 1

The Correct Option is A

To find the correct mean of the numbers after correcting the wrongly recorded number, we will follow these steps:

1. First, calculate the total sum of the 9 numbers using the given mean:
   • The formula for mean is: \(\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Items}}\)
   • Given mean = 50, Number of Items = 9
   • Using the formula: \(50 = \frac{\text{Total Sum}}{9}\)
   • So, \(\text{Total Sum} = 50 \times 9 = 450\)
2. Identify and correct the wrongly recorded number:
   • The wrongly recorded number is 63, which should be 36.
   • Remove 63 from the total sum and add 36 to get the correct total.
   • Corrected Total Sum = \(450 - 63 + 36 = 423\)
3. Calculate the correct mean using the corrected total sum:
   • Use the formula for mean again with the corrected total sum: \(\text{New Mean} = \frac{423}{9}\)
   • Calculate: \(423 \div 9 = 47\)

The correct mean is 47.

Let's verify the decision with the given options:

• Option 47: Correct
• Option 48, 49, 50: Incorrect based on our calculations

Hence, the correct answer is 47.