you simply need to know that standard deviation is a representation of how far away from the mean the values of a set are.
So the standard deviation of 5,5,5,5,5 is smaller (it's in fact 0) than the standard deviation of 4,5,5,5,6 even though both have the same mean.
The key to this question is that we know the average, and that both sets contain at least 3 of the same numbers.. so:
Set S: [30,40,50,_,_]
Set T: [30,40,50,_,_]
For 1:
S: [25,30,40,50,_]
Give that we know the average is 40, the 5th number must be 55. So S: [25,30,40,50,55]
But we don't know anything about T, so INSUFF
For 2:
T: [_,30,40,45,50]
Give that we know the average is 40, the 5th number must be 35. So T: [30,35,40,45,50]
But we don't know anything about S, so INSUFF
Together, we can look and see that the two values that differ between S and T are a bit more spread out with S... so S will have a larger standard deviation. SUFF
std deveation
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An easy way to think about it is that you know that the average of each set is 40, and three numbers from each set are given to you.
Thus you know that the sets look something like this:
S = { ......30......40.......50........}
T = { ......30......40.......50........}
At this point you know that the average is 40, so in both sets the numbers have to be balanced on both sides of 40, the real question is whether the two integers that balance one set are further away from 40 than the other For example the two numbers left out could be anything such as 10 and 70 or 39 and 41. Clearly 10 and 70 would result in the larger standard deviation.
Statement 1: Knowing that 25 is in list S allows you to conclude that set S consists of the following:
S = { 25,30,40,50,55 }
You still don't know where the two balancing integers in T sit, so this is not sufficient. If T's missing numbers are 39 and 41, the standard deviation in T is less, but if they are 20 and 60, the standard deviation in T is greater.
Statement 2: By itself is just the reverse of statement 1- you can round out T as the following:
T = { 30,35,40,45,50 }
but you don't know what balances S.
Taken together, clearly you have enough info. The standard deviation of S is greater than T.
Thus you know that the sets look something like this:
S = { ......30......40.......50........}
T = { ......30......40.......50........}
At this point you know that the average is 40, so in both sets the numbers have to be balanced on both sides of 40, the real question is whether the two integers that balance one set are further away from 40 than the other For example the two numbers left out could be anything such as 10 and 70 or 39 and 41. Clearly 10 and 70 would result in the larger standard deviation.
Statement 1: Knowing that 25 is in list S allows you to conclude that set S consists of the following:
S = { 25,30,40,50,55 }
You still don't know where the two balancing integers in T sit, so this is not sufficient. If T's missing numbers are 39 and 41, the standard deviation in T is less, but if they are 20 and 60, the standard deviation in T is greater.
Statement 2: By itself is just the reverse of statement 1- you can round out T as the following:
T = { 30,35,40,45,50 }
but you don't know what balances S.
Taken together, clearly you have enough info. The standard deviation of S is greater than T.
