Question : The average of 100 observations was calculated as 35. It was found later, that one of the observations was misread as 83 instead of 53. The correct average is:
Option 1: 32.7
Option 2: 34.7
Option 3: 35.7
Option 4: 36.7
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Correct Answer: 34.7
Solution :
Given: The average of the 100 observations = 35
So, the sum of 100 observations = 100 × 35 = 3500
The correct value is 53 and the incorrect value is 83.
Difference = 83 – 53 = 30
So, the correct average = $\frac{3500–30}{100}$ = $\frac{3470}{100}$ = 34.7
Hence, the correct answer is 34.7.
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