Question : The average of 18 integers is found to be 41. It was detected that by mistake the integer 127 was copied as 341 while calculating the average. Then the correct average is:
Option 1: $23 \frac{1}{7}$
Option 2: $33 \frac{1}{9}$
Option 3: $29 \frac{1}{9}$
Option 4: $37 \frac{1}{3}$
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Correct Answer: $29 \frac{1}{9}$
Solution :
Given that:
Average of $18$ integers = $41$
Also, the integer $127$ was copied as $341$ by mistake
we know, Average = $\frac{\text{Sum of integers}}{\text{Count of integers}}$
So, $41=\frac{\text{Sum of integers}}{18}$
⇒ Sum of Integers = $738$
And new sum $= 738+127-341=524$
Hence, the new average $=\frac{524}{18}= 29 \frac{1}{9}$
Hence, the correct answer is $29 \frac{1}{9}$.
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