kevincan wrote:

S and T are sets of numbers. The standard deviation of the elements of set S is q. Is the standard deviation of S U T greater than q?

(1) The range of S U T is different from the range of S.

(2) There is only one element in T, and it is twice the arithmetic mean of the elements in S.

going with C.

Just starting out with math, so am just trying to nail down the concepts.

1: The range can only change in a set if the difference between the greatest elements in the set changes. Since the new set SUT contains all the elements of the old set S, the range of the new set, if different, must be greater, since it cannot be smaller. However we are concerned not with range but with SD. There may be 5 elements in S and 1000 elements in T. One element in T is greater than the largest elememt in S or lesser than the smallest in S, increasing the range. This one element will certainly cause the SD to increase. The other 999 elements may actually be the same value as the arithmetic mean, thereby reducing the SD.

We cannot say from 1, if the SD will increase or decrease, though we can say that the range will increase.

2: There is a single element in T which is twice the average. Consider a set as follows:-

{ 0, 10000}

Now add another element which is twice the mean, i.e. 10000

Since the question does not say the sets are disjoint, this is possible.

Set SUT = S = { 0, 10000 }, and the SD does not change.

Consider another set S {0,10,20} mean = 10, SD = 5.something.

Add an element twice the mean i.e. 20. SD increases.

Therefore 2 is incufficient.

Consider 1 and 2 together. If there is one element added, and this causes the range to increase, it cannot be an element already in S. Then, SD will increase.

Will go with C