Question : The average of 100 items was found to be 30. If, at the time of calculation, two items were wrongly taken as 32 and 12 instead of 23 and 11, then the correct average is:
Option 1: 29.8
Option 2: 29
Option 3: 29.9
Option 4: 29.5
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Correct Answer: 29.9
Solution : Given: The average of 100 items is 30. Sum of all items = 100 × 30 = 3000 A wrong entry of 32 and 12 instead of 23 and 11 is also included. The difference made by the wrong entry of 32 and 12 instead of 23 and 11 = (32 + 12) – (23 + 11) = 10 So, the actual sum = (3000 – 10) = 2990 Average value = $\frac{\text{Sum of observations}}{\text{Total no. of observations}}$ So, Average of the items = $\frac{2990}{100}$ = 29.90 Hence, the correct answer is 29.90.
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