Question

The mean age of 12 boys is 8 years later it was
found that the age of one boy was taken as 13 years
in place of 10 years find the actual mean of their ages.​

Answer 1

Answer:-

Given:

Mean age of 12 boys = 8 years.

We know that,

Mean = sum of observations/Number of observations.

Hence,

Sum of ages of 12 boys / 12 = 8

→ Sum of ages of 12 boys = 8 * 12

→ Sum of ages of 12 boys = 96 years

And,

Later it was found that the age of one of the boys is taken as 13 years instead of 10 years.

Let us assume that,

Sum of ages of remaining 11 boys = y.

→ y + 13 = 96

→ y = 96 - 13

→ y = 83 years

→ Sum of ages of 11 boys = 83 years.

Now,

Actual mean age = (sum of ages of 11 boys + actual age of 12th boy) / 12

→ Actual mean age = (83 + 10) / 12

→ Actual mean age = 93/12

→ Actual mean age = 7.75 years

Therefore, the actual mean of their ages is 7.75 years.

Answer 2

Answer:

Mean of 12 Students is 8 years.

One Boy age was taken as 13 years in place of 10 years. So that (13 - 10) = 3 years is taken from other 12 Boys. Now we must return that age to them.

⇒ 3/12 = 1/4 = 0.25 years

• Actual Mean of Boys :

⇢ Mean = Wrong Mean - Alteration Age

⇢ Mean = 8 years - 0.25 years

⇢ Mean = 7.75 years

∴ Hence, Actual Mean of Boys is 7.75 years.