gmat1220 wrote:
I guess the answer is SD(second) > SD (third). Pls can you shed some light on the range of the data - I made two observations about the third set -
a. the third set has more numbers. So this decreases the SD.
Actually, you generally cannot decide anything based on how many numbers there are. e.g if a set has 4 numbers, all very far from each other and another set has 3 numbers very close to each other, the SD of the set with 3 numbers will be smaller. The point is how dispersed the numbers are.
In the diagram above, in the second set, the numbers are far away from each other. In the third set, the numbers are closer to each other. Hence SD of second set > SD of third set.
If there are two sets A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6}, here SD of B > SD of A. The reason again is not directly linked to the fact that B has more numbers. SD of B is higher because it has numbers that are farther away from the mean. The mean of B is 3.5 and numbers 1 and 6 are 2.5 away from the mean. In set A, the extreme terms are only 1.5 away from the mean.
There are cases where just the number of terms could decide the SD. e.g.
A = {1, 1, 3, 5, 5}, B = {1, 3, 5}
Here, there are more terms which are far from the mean hence SD of A > SD of B
My suggestion would be to plot the numbers on the number line, mark the mean there and see in which set the values are more dispersed from the mean. The values will be such that you will get a very clear idea.