The average of 100 observations is 35. Later it is found that one observation was misread as 83 instead of 53. What is the correct average of the 100 observations after fixing this error? Give the exact corrected average as a decimal.

Introduction / Context:
This question tests error correction in averages. The average is defined as total sum divided by the number of observations. If one value is recorded incorrectly, the computed total sum becomes wrong by exactly the difference between the wrong value and the correct value. Instead of recomputing everything, you adjust the total sum by subtracting the extra amount (or adding the missing amount) and then divide again by the same number of observations. This is a very common aptitude pattern because it rewards recognizing that only one term changed, so the correction is quick and direct.

Given Data / Assumptions:

• Number of observations, n = 100 • Given average (based on misread data) = 35 • One observation was taken as 83 but should be 53 • Required: corrected average

Concept / Approach:
Compute the (incorrect) total sum using average * number of observations. Then correct that sum by removing the extra amount added due to misreading. Here, 83 instead of 53 means the total was too high by (83 - 53) = 30. Subtract 30 from the total, then divide by 100 to get the correct average.

Step-by-Step Solution:
1) Compute the total sum used originally: Sum_wrong = 35 * 100 = 3500 2) Find the error in the one observation: Error = 83 - 53 = 30 (sum is 30 too high) 3) Correct the total sum: Sum_correct = 3500 - 30 = 3470 4) Compute corrected average: Average_correct = 3470 / 100 = 34.7

Verification / Alternative check:
A quick sense check: because the misread value (83) is larger than the correct value (53), the original average 35 must decrease after correction. The corrected average 34.7 is slightly smaller (by 0.3), which matches the fact that the total decreased by 30 over 100 observations (30/100 = 0.3). This confirms both the direction and size of correction.

Why Other Options Are Wrong:
• 35.7 and 36.7: move in the wrong direction (average should go down, not up). • 32.7: would require a much larger correction (a 230 drop in total, not 30). • 34.3: corresponds to subtracting 70 instead of 30.

Common Pitfalls:
• Adding the error instead of subtracting it. • Dividing the error by 100 twice or not at all. • Recomputing using 83 + 53 (wrong idea) instead of using the difference.

Final Answer:
34.7