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?

2 Answers
Aug 11, 2016

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.!

Aug 11, 2016

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