The average of 100 items is found to be 30. During the calculation two items were wrongly taken as 32 and 12 instead of 23 and 11. What is the correct average of the 100 items?

Introduction / Context:
This question involves correcting an average when two observations have been entered incorrectly. Such data correction problems are very common in aptitude and data interpretation sections. The key is to adjust the total sum using the correct and incorrect values and then recompute the average.

Given Data / Assumptions:

• The reported average of 100 items is 30.
• Two items were mistakenly taken as 32 and 12.
• The correct values for those two items are 23 and 11.
• We need to find the correct average of all 100 items.

Concept / Approach:
Average equals total sum divided by number of items. The reported average is based on an incorrect total. We first find this incorrect total by multiplying average by number of items. Then we remove the wrong values and add the correct values to get the corrected total. Finally, we divide the corrected total by 100 again to obtain the correct average.

Step-by-Step Solution:
Step 1: Incorrect total sum = reported average * number of items = 30 * 100 = 3000. Step 2: The wrong values used were 32 and 12, whose total is 32 + 12 = 44. Step 3: The correct values are 23 and 11, whose total is 23 + 11 = 34. Step 4: To correct the total, subtract the wrong total and add the correct total: corrected total = 3000 - 44 + 34. Step 5: Compute 3000 - 44 = 2956, then 2956 + 34 = 2990. Step 6: Correct average = corrected total / number of items = 2990 / 100 = 29.9.

Verification / Alternative check:
Notice that the net effect of the error on the total is 44 - 34 = 10 extra marks added by mistake. Therefore, the corrected total should be 3000 - 10 = 2990, which matches our detailed calculation. Dividing by 100 gives 29.9, so the answer is consistent by two different checks.

Why Other Options Are Wrong:
Option 29.8 would correspond to a total of 2980, which is 10 less than the correct total. Option 29 would require a total of 2900, implying an error of 100 marks. Option 29.5 would imply a total of 2950. None of these match the precise net correction of 10 marks from the given wrong and correct values.

Common Pitfalls:
Some learners mistakenly average the wrong and correct values or adjust the average directly by the difference divided by number of changed items rather than the total number of observations. The safe method is always to work with the total sum, apply the correction, and then recompute the average with the full sample size.

Final Answer:
The correct average of the 100 items is 29.9.