The mean of 50 observations is 36. Later it is found that one observation was recorded as 23 instead of 48. What is the corrected mean of the 50 observations?

Introduction / Context:
This aptitude question checks your understanding of how a single incorrect value affects the mean of a data set. You are given the original mean of 50 observations and told that one value was recorded wrongly. You must recalculate the corrected mean after fixing that erroneous observation. This type of problem is common in exams for bank jobs, SSC and campus placements because it combines ideas of averages and error correction.

Given Data / Assumptions:
- Number of observations = 50.
- Original mean (with error) = 36.
- Wrongly taken value = 23.
- Correct value should be = 48.
- We need to find the new corrected mean of all 50 observations after replacing 23 by 48.

Concept / Approach:
The mean of n observations is defined as total sum divided by n. If one value in the set is changed, the total sum changes by the difference between the new and the old value. Here, instead of recomputing everything from scratch, we can adjust the original total sum by adding the correction difference and then divide again by 50 to obtain the corrected mean.

Step-by-Step Solution:
Step 1: Original total sum with error = mean * number of observations = 36 * 50 = 1800.Step 2: Because 23 was recorded instead of 48, the total is short by 48 - 23 = 25.Step 3: Corrected total sum = 1800 + 25 = 1825.Step 4: Corrected mean = corrected total sum / number of observations = 1825 / 50.Step 5: 1825 / 50 = 36.5.

Verification / Alternative Check:
You can also think directly in terms of the effect on the mean. The total has increased by 25 while the number of observations is still 50. So the mean should increase by 25 / 50 = 0.5. The original mean was 36, so the corrected mean must be 36 + 0.5 = 36.5. This fast reasoning matches the detailed calculation and confirms that 36.5 is correct.

Why Other Options Are Wrong:
A mean of 35 would be smaller than the original 36, which is impossible because the correction increased the total. Means of 40 and 42 are much too high and would require a much larger increase in total sum than the given difference of 25. Therefore those values do not agree with the actual change in the data set.

Common Pitfalls:
Students sometimes subtract 25 instead of adding it, or they divide the difference by 49 or 51 instead of 50. Another mistake is to try to adjust the mean directly without understanding that it is the total sum that changes first. Always start from total = mean * number of observations, correct the total, and then divide by the same number of observations.

Final Answer:
The corrected mean of the 50 observations is 36.5.