Question : The average of nine observations was found to be 35. Later on, it was detected that observation 81 was misread as 18. The correct average of the observations is:
Option 1: 28
Option 2: 42
Option 3: 32
Option 4: 45
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Correct Answer: 42
Solution :
Given: The average of 9 observations was found to be 35.
The sum of all observations = 9 × 35 = 315
A wrong entry of 18 instead of 81 is also included.
The difference made by the wrong entry of 18 instead of 81 = 81 – 18 = 63
So, the actual sum = 315 + 63 = 378
The average of observations = $\frac{\text{Sum of the observations}}{\text{Total number of observations}}$
So, the average of 9 observations = $\frac{\text{378}}{\text{9}}$= 42
Hence, the correct answer is 42.
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