Question

The average of four three-digit numbers was calculated to be 335. However, it was realized that the digit '8' was misread as '3' in the second position of one number and in the third (last) position of another number. What would be the average of these four numbers after correcting this mistake?

• A. 340.55
• B. 348.75
• C. 350.5
• D. 358.75

Answer 1

Answer:

B. 348.75

The correct average is 348.75.

Here is the step-by-step solution:

1. Find the current total sum

Since the average of 4 numbers is 335, their total sum is:
$4 \times 335 = 1340$

2. Calculate the difference from the mistakes

There were two errors where an '8' was misread as a '3':

• Error 1 (Tens position): A '3' was recorded instead of an '8'. This means the value was undercounted by 50 ($80 - 30 = 50$).

• Error 2 (Units position): A '3' was recorded instead of an '8'. This means the value was undercounted by 5 ($8 - 3 = 5$).

Total value to be added back: $50 + 5 = \mathbf{55}$.

3. Calculate the new total sum

Add the missing values to the initial sum:
$1340 + 55 = 1395$

4. Calculate the correct average

Divide the new total by the number of values (4):
$\frac{1395}{4} = 348.75$