ds/mean

[advita]

If sets S and T are united into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1.S and T are one-element sets
2.Neither set S nor set T contains negative numbers


my query: what is mean of single element.

...i think it is the element itself. i.e for t={5} mean is 5.

just for confirmation. is it true.???

OA-..E

[arora007]

You are right...single element set would have the from t={5}

and with this this, I part ways with the OA.

the OA should be A, clearly.

t={5} now individual mean is 5
v={7} now individual mean is 7

their average is (5+7)/2 = 6

now t U v = {5,7} now the mean of this set is (5+7)/2 = 6.

[gmat1011]

that is what "one element sets" should mean... the number is its own mean.

Here we can rules out B coz if set s and set t have only zeros... then stem 2 is disproved... you get Y if sets S and T have only +ve numbers and a N if sets S and T are made up of only zeros.

As regards A it gets disproved if you consider s and t to be both +ve and then both -ve... you get opposite results.

Together: again with only +ve one element sets you get a y and with only 0 in both sets you gets a N. so E.

[arora007]

As regards A it gets disproved if you consider s and t to be both +ve and then both -ve... you get opposite results.

did not get that... how?? maybe an example...

[gmat1011]

Hi, For considering stem 1:

+VE one set elements only

S= 5
T = 6

Sum of individual means = 11
Mean of combined set = 11/2 = 5.5

So sum of means > mean of combined

-VE one set elements only

S= -5
T= -6

Sum of individual means = -11
Mean of combined set = -11/2 = -5.5

So mean of combined > sum of means

[jaxis]

As regards A it gets disproved if you consider s and t to be both +ve and then both -ve... you get opposite results.

did not get that... how?? maybe an example...

Arora,

How abt this example...S = {0} , T = {0}

here, mean of individual set = mean of combined set.

This example can help u in Statement 2 also.

[arora007]

I might have been asleep!! you guys are right...

sum of means.. and not average of the sum of means...