Mean of two sets

[goelmohit2002]

Hi All,

When two sets A and B are combined, then mean of set C lies between mean of set A and B.

E.g. if mean of set A = 2
if mean of set B = 5
then 2 <= mean of C <= 5.

Can someone please tell why ? Why mean lies between these two figures ?

Thanks
Mohit

[jatharnikhil]

Consider two sets:
A = {1,2,3} -> mean = 2
b = {3,4,5,6,7} -> mean = 5

if you combine these two sets, you will get {1,2,3,3,4,5,6,7} -> mean = (6 + 25)/8 = 31/8 ~ 3.88.

now why?

Because mean is the average of the numbers. Now first set has average '2' while second one has '5'. Therefore, if you add both you won't be able to get avargare which is less than '2' or greater than '5' (because 2 is minimum avarage here, while second set average is '5').

now to clarify this, add few numbers in first set and change its avarage:

A = {8,4,4,1,3} = 20 -> mean = 4
b = {3,4,5,6,7} = 25 -> mean = 5

now check again 20 + 25 / 10 => 4.5 (which is greater than 4 and less than 5).

I hope it helps. :)


-
Kind Regards,
Nikhil J.
student/GMAT Enthu/ www.nikhilj.com

[Ben Ku]

Suppose set X has 6 values, with average 12. The sum of all the values is 72.
Suppose set Y has 4 values, with average 15. The sum of all the values is 60.

If we want to find the average of the combined set of X+Y:
average = (sum X + sum Y) / (no X + no Y) = (72 + 60) / (6 + 4) = 13.2

As you observed, the average of the combined set is between the average of the individual sets.

Note that as I am doing this calculation, it doesn't really matter what the individual values in the sets are; I am only concerned about their sums.

Let's look at the same problem another way.

If set X has 6 values with average 12, we might as well make all six value 12. It will produce the same result.
If set Y has 4 values, with average 15, we might as well make all four values 15.

If we average six 12's and four 15's, it make sense that the average will be between 12 and 15. It won't be less than 12 because we have no values less than 12; it won't be greater than 15 because there are no values greater than 15.

Hope this makes sense.