Narenn wrote:
Fantastic Question from
VERITAS.
Explain in detail and get a Kudos Reward
.
Is the standard deviation of set A is greater than standard deviation of set B ?
1) Set A consists of consecutive multiples of 10
2) Set B consists of consecutive multiples of 2
OA and OE after sufficient discussion.
Happy Solving!!
OA has to be E.
Statement 1 doesn't tell us about the standard deviation of B.
Statement 2 alone doesn't tell us anything about standard deviation of A.
Combining its still insufficient to prove that the SD of A is more than B.If the question would have told us the number of members in each series then both statement together would have been sufficient. Why? See explanation below.
Just pick any number and you will see that the SD of A is always more than B.
Take number 1,2,3,4,5,6....These numbers are neither the consecutive multiple of 2 nor they are consecutive multiples of 10.
However if you multiply them by 2 then you will get 2,4,,6,8,10....
If you multiply the same series by 10 then you will get 10,20,30,40,50,60
So the standard deviation in the consecutive multiples of 10 is always more than consecutive multiples of 2.
Universal rule....Suppose a series of number is A,B,C,D,E,F.....
if you multiple that series by same number then the standard deviation will rise. If you divide the whole series by the same number then SD will reduce.
In the case of multiples of 10 you are basically dividing the whole series by 5 to get consecutive even multiples. Now you might argue that the numbers are not the same in both series. Numbers doesn't matter as we are checking the SD against the mean.
Take example:
10,20,30,40,50,60,70.....consecutive multiples of 10.
2000,2002,2004,2006,2008.....consecutive multiples of 2.
So which one has lower SD. Obviously multiples of 2. So even if the number in consecutive multiples of 2 are bigger we still get SD smaller than consecutive multiples of 10.
To the original question:You can have multiples of 10 as 10,20...thats it two members.
You can have multiples of 2 as 2,4,6,8,10,12,...2000 in this case SD of the latter is more.
So the final answer is E