Online Question Bank : Word Problems : #4

I went over the online solution and noticed that in this solution some statistics rules are presented that had not been in the guide.

I was just wondering if there are other rules that you think it would be good to know related to statistics and standard deviation.

Also I wonder if you might have any suggestions of a method to solve these types of problems.

The table below represents three sets of numbers with their respective medians, means and standard deviations. The third set, Set [A+B], denotes the set that is formed by combining Set A and Set B.

Median Mean StandardDeviation
Set A X Y Z
Set B L M N
Set [A + B] Q R S

If X – Y > 0 and L – M = 0, then which of the following must be true?

I. Z > N
II. R > M
III. Q > R


I only
II only
III only
I and II only
none

In general, you should definitely know how to handle both average (mean) and median. Standard deviation is necessary if you want a high score.

Some of the discussion in the explanation for this problem is basic to understanding what median and mean represent. For example, if the median of a set of numbers is greater than the mean of that same set - this just means that the numbers below the median must be farther from the median than the numbers above - eg 1, 3, 4, 16, 17, 18, 19, the median is 16 and the mean is 11.1. If the median is smaller than the mean, then the numbers above the median must be farther from the numbers below - just the opposite of the previous example.

Also know that there are some relationships between mean and median when you have a set of consecutive integers (must be consecutive). If you have a set of consecutive integers, then you can find the average by just averaging the first and last terms. For example, 1, 2, 3, 4, 5. For the average, I can just take (1+5)/2 = 3. If the set has an odd number of consecutive terms, then the median will also equal the mean. In that last example, 3 is both the median and the mean.

The rule given for a "composite set" in this explanation is a more obscure rule, however. Only worry about remembering that if you want a 700+ score. (Notice that this problem is labeled 700-800; it's a very hard problem.)