Question : The mean of 100 items was 46. Later on, it was discovered that item 16 was misread as 61 and another item, 43, was misread as 34. It was also found that the number of items was 90 and not 100. Then, what is the correct mean?
Option 1: 50
Option 2: 50.7
Option 3: 52
Option 4: 52.7
Correct Answer: 50.7
Solution :
Given:
The average of 100 items is 46.
An entry of 16 was misread as 61.
Another entry of 43 was misread as 34.
Total items were 90, not 100.
The sum of 100 items = 100 × 46 = 4600
Difference made by the wrong entry of 61 instead of 16 = 61 – 16 = 45 (extra)
Difference made by the wrong entry of 34 instead of 43 = 43 – 34 = 9 (less)
Actual sum of 90 items = 4600 – 45 + 9 = 4564
Average of 90 items =
Hence, the correct answer is 50.71.
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