Problem Solving

Set X and Y have 5 numbers, respectively.Is the S.D of X > S.D of Y?
1) Range of X > Range of Y
2) Average of X is greater than that of Y

What should be the answer here?

prachi18oct wrote:Set X and Y have 5 numbers, respectively.Is the S.D of X > S.D of Y?
1) Range of X > Range of Y
2) Average of X is greater than that of Y

What should be the answer here?

Statements combined:
Case 1: X = {10, 10, 10, 10, 20} and Y = {10, 10, 10, 10, 10}
Average of X = 12, with the result that one data point (20) deviates FAR from the mean.
Average of Y = 10, with the result that NO data points deviate from the mean.
Thus:
SD of X > SD of Y.

Case 2: X = {0, 13, 13, 14, 20} and Y = {0, 2, 10, 19, 19}
Average of X = 12, with the result that most of the data points (13, 13, 14) stay CLOSE to the mean.
Average of Y = 10, with the result that most of the data points (0, 2, 19, 19) deviate FAR from the mean.
Thus:
SD of X < SD of Y.

The correct answer is E.

The answer is E...


Statement 1 - The range has not affect on the standard deviation.
Statement 2 - If a set has all the same numbers the standard deviation is 0. Why do I mention that? If you think of a group of large numbers that are all the same the S.D. would be 0, and less than the S.D. of a bunch of small numbers that are different. You could switch the scenario as well by making all of the smaller numbers the same and the larger numbers different.


Together - As the size of the numbers (thinking about statement 2) does not affect the standard deviation adding the notion of range, which also does not affect S.D., does not influence this either.

prachi18oct wrote:Set X and Y have 5 numbers, respectively.Is the S.D of X > S.D of Y?
1) Range of X > Range of Y
2) Average of X is greater than that of Y

What should be the answer here?

Statement 1 gives us nothing. Range is not connected to standard deviation.
Statement 2 gives us the mean, but does not tell anything about the different terms.

So, we cannot find the distance between the mean and each term and in turn, we cannot find the S.D.

Combining the two also we cannot say anything.

Hence E is the answer