Question

the average age of a class of 20 boys 14.95 years.the average age of the class is raised to 15 years by the comming of a new boy.what is the age of the new boy.

Answer 1

Average age of class of 20 boys is 14.95
=X1+X2+......Xn/20

Now new average =X1+X2+.........X(n+1)/21
=X1+X2+......Xn/21+X(n+1)/21
15=20*14.95/21+ X(n+1)/21
15=[299 + X(n+1)]/21
15*21-299=X(n+1)
X(n+1)=315-299
=16
Answer is 16
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Answer 2

we know that whichever operation is done on the mean the same operation is done on the observations
let's take the weight of the new boy be x.
therefore mean + increased value I. mean= sum of obs of 20 boys + weight of new boy divided by 21
sum of weight of 20 boys are
$sum =14.95 \times 20$
so
$\frac{14.95 + 15}{1} = \frac{14.95 \times 20 + x}{21}$