Question

Anita has two sisters and three brothers. The mean of all their ages is 6 years. What will their mean age be 10 years from now? Twenty years from now?

Answer 1

10 years from now, it will be 16

20 years from now, it will be 26

Explanation:

Right now, their ages are: `{a_1, a_2, ..., a_N}` with mean age:

`bar a = (sum_1^N a_i)/N`

In `n` years time, ages will be: `{a_1 + n, a_2 + n ... a_N + n}`, with mean age :

`bar a_n = (sum_1^N (a_i + n))/N = (sum_1^N (a_i) + (Nn))/N`

`= (sum_1^N (a_i))/N + n = bar a + n`

IOW, `bar a_n = bar a + n`, or:

• 10 years from now, ave age will be 16

• 20 years from now, ave age will be 26