In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean.

In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean. 

Answer Details

Let's call the sum of the 8 numbers as S. Then, the boy's calculation of the mean is: $$ \text{Mean} = \frac{S+17}{8} $$ However, the correct calculation of the mean should be: $$ \text{Correct Mean} = \frac{S+25}{8} $$ We know that the boy obtained 20 as the mean, so we can set the two expressions equal to each other and solve for S: $$ \frac{S+17}{8} = 20 \implies S+17 = 160 \implies S = 143 $$ Therefore, the correct mean is: $$ \text{Correct Mean} = \frac{S+25}{8} = \frac{143+25}{8} = \frac{168}{8} = 21 $$ So the correct mean is 21. Therefore, the answer is (3) 21.