Question

The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is

• A. 32
• B. 36
• C. 38
• D. 42

Hint:

When correcting a mean due to misread observations, start by finding the incorrect total sum. Then, adjust this sum by subtracting the wrong values and adding the right ones. Finally, divide the new, correct sum by the number of observations. In this specific case, the sum of the incorrect values (25+36=61) happens to be equal to the sum of the correct values (23+38=61), so the total sum and the mean do not change.

Answer 1

The Correct Option is C

Step 1: Find the incorrect sum of observations.
Mean = \( \frac{\text{Sum of observations}}{\text{Number of observations}} \)
Incorrect Mean = 38. Number of observations = 25. Incorrect Sum = Incorrect Mean \( \times \) Number of observations = \( 38 \times 25 = 950 \).

Step 2: Correct the sum. The incorrect sum includes the misread values. To get the correct sum, we subtract the incorrect values and add the correct values.
Incorrect values that were added: 25 and 36. Sum = 61.
Correct values that should have been added: 23 and 38. Sum = 61.
Correct Sum = Incorrect Sum - (Sum of incorrect values) + (Sum of correct values)
Correct Sum = \( 950 - (25 + 36) + (23 + 38) \)
Correct Sum = \( 950 - 61 + 61 = 950 \).

Step 3: Calculate the correct mean. The sum of observations did not change.
Correct Mean = \( \frac{\text{Correct Sum}}{\text{Number of observations}} = \frac{950}{25} = 38 \).
The mean remains 38.