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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

Answer:

#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

Answer:

#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#