The mean of 100 observations is 40. Later it is found that one observation was misread as 48 instead of the correct value 84. What is the correct mean of the 100 observations after this error is rectified?

Introduction / Context:
This problem focuses on correcting a mean when one observation was recorded incorrectly. Questions of this type are common in statistics and data interpretation, where a misread or misprinted value must be adjusted without recomputing the entire data set from scratch.

Given Data / Assumptions:
- Number of observations = 100.
- Reported mean = 40.
- One value was recorded as 48 but should have been 84.
- Only this single misread value needs correction.

Concept / Approach:
The mean is defined as:
Mean = (Sum of all observations) / (Number of observations)
From the given mean and count, we can reconstruct the total sum. Then we subtract the wrong value and add the correct value to adjust the total, and finally recompute the corrected mean.

Step-by-Step Solution:
Step 1: Let S be the sum of all 100 observations as originally recorded.Step 2: Using the reported mean, S = 40 * 100 = 4000.Step 3: The value 48 is wrong and should be 84. So remove 48 and add 84.Step 4: Corrected sum S_correct = 4000 - 48 + 84.Step 5: Compute S_correct = 4000 - 48 + 84 = 4000 + 36 = 4036.Step 6: Corrected mean = S_correct / 100 = 4036 / 100 = 40.36.

Verification / Alternative check:
The adjustment to the total is equal to the difference between the correct and wrong values: 84 - 48 = 36. Dividing this by 100 gives an increase in the mean of 0.36. The old mean was 40, so the new mean is 40 + 0.36 = 40.36, which confirms the result without recomputing the entire sum.

Why Other Options Are Wrong:
- 41.24, 41.92 and 42.05 all represent much larger corrections to the mean than 0.36. These would imply a much bigger difference between the wrong and correct values, which is not the case here.

Common Pitfalls:
- Forgetting to remove the wrong value from the total before adding the correct value, and instead just adding the difference incorrectly.
- Dividing the correction 36 by the wrong number of observations, for example by 1 instead of 100.
- Misinterpreting the question and recalculating with 101 observations or 99 observations.

Final Answer:
The corrected mean of the 100 observations is 40.36.