Question

The mean of 3 numbers is 7. The mean of 4 other numbers is 8. The mean of 5 other numbers is 11. What is the mean of all 12 numbers?

Answer 1

`9`.

Explanation:

Let `barx_i` be the mean of a group `G_i` of `n_i` observations,

where, `i=1,2,3,...,m`.

Then, the mean `barx` of the combined group

`G=G_1uuG_2uuG_3uu...uuG_m` is given by,

`barx=(Sigma_(i=1)^(i=m) n_ibarx_i)/(Sigma_(i=1)^(i=m) n_i`.

We have, `n_1=3, n_2=4, n_3=5, barx_1=7, barx_2=8,barx_3=11`.

Hence, `barx=(3*7+4*8+5*11)/(3+4+5)=108/12=9`, as derived by

Lyn. !

Enjoy Maths.!

Answer 2

`9`

Explanation:

To work out the mean (what we understand as the 'average') we do the following;

`Mean = (" sum (total) of all the values")/("the number of values")" OR " " M=T/N`

As with other formulae in this form, we have 3 ways in which it can be used.

`M = T/N " "T = MxxN" " N = T/M`

Remember that we may add Totals , we may add Numbers , but we may NOT ADD MEANS!

The mean of 3 numbers is 7 .
`"There are 3 numbers, the mean is 7," rArr "the total is " 3xx7 = 21`

The mean of 4 numbers is 8
`"There are 4 numbers, the mean is 8," rArr "the total is " 4xx8 = 32`

The mean of 5 number is 11
`"There are 5 numbers, mean is 11" rArr "the total is "5xx11=55`

We can add numbers: `3+4+5 =12`

We can add totals: `21+32+55=108`

We can find the mean of the 12 numbers: `M = 108/12 = 9`