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# GMAT Statistics

by ejkiv

July 19, 2015

GMAT Statistics. It is probably one of the most hated classes in the entire business school experience. Luckily, you don’t have to worry about a lot of the complexities for quite some time, however this is a section that is getting more play in exams lately, in fact you are likely to see 2 or 3 questions on this topic come exam day. Average is the one concept that is covered, and we have already covered 2 sections related to this subject. Here are a few more:

Range: The difference between the largest value of a set and the smallest value of a set.

The range of the set {2,3,5,7,10} is 8, which comes from 10-2.

Median: The middle number of a set. If there are an even number of terms, it is the average of the two middle most terms in the set.

The median of the set {2,3,5,7,10} is 5 because it is the middle term. The median of the set {2,3,5,7,7,10} is 6 because the average of the two middle terms, 5 and 7, is 6.

A special type of set is one that is evenly spaced. {1,2,3,4,5} or {10, 20, 30} or {150, 300, 450, 600} or {11,13,15,17} are all evenly spaced sets. We discussed this earlier, but there is still a small amount of information to add with our new terminology: The median will always equal the mean. Even better than this is the fact that the mean and median can be calculated from taking the average of the first and the last term if you can find the median by traditional methods. This will become a great shortcut on longer problems.

Mode: The number that occurs most in a set

The mode of the set {2,3,5,7,7,10} is 7. There can be more than one mode. In the set {2,2,3,3,7,10} both 2 and 3 are modes of this set.

The final piece of statistics that has been creeping up more and more on the GMAT is standard deviation. You will not have to calculate standard deviation (you can wait until your 1st year stats class for that) but you should know how it is calculated and what exactly it stands for.

Standard Deviation: A measure of how spread out numbers are. This can also be describe as variability.

Variance: The square of standard deviation.

I threw variance in there because it is so closely related to standard deviation. Let’s look at an example calculation with a few sets just to understand it a bit better;

A = {3, 4, 5, 6, 7}

B = {10, 10, 20, 30, 30}

The first thing that you will need to know is the mean of each set; in this case, the mean of A is 5 and B is 20. You can probably see that the numbers in A are closer to the mean than in set B, and this is likely how you will have to evaluate things on the GMAT; however, we will still go through the calculation.

To calculate standard deviation you need “the average of the sum of the squared differences from the mean.” It sounds like a mouth full, but in practice it isn’t so bad. Start with the squaring the differences from the mean for each set:

The sum of the differences in Set A is 10 and in Set B is 400.  The average difference is equal to the variance, or 2 for Set A and 80 for Set B. The standard deviation is simply the square root of variance or sqrt(2) for set A and sqrt(80) for set B. Here is what the entire calculation looks like for set A, just so you can see.

And because variance is just the square of standard deviation it is 2. Again, you will not have to calculate this for the exam, but it is worth remembering how to do if for no other reason than you will see it again. In actuality, knowing it will prepare you better for any question you may face.

The next question that you will face is related to the number of standard deviations from the mean. If a set had an average of 50 and a standard deviation of 5 then each standard deviation is spaced 5 above or below the mean of 50. Thus, one standard deviation above the mean is 55 and two standard deviations above is 60. Similarly, 1 standard deviation below the mean is 45 and two standard deviations below is 40.

Within one standard deviation: 50 ± 5 or between 45 and 55

Within two standard deviation: 50 ± 5(2) or between 40 and 60

Within three standard deviation: 50 ± 5(3) or between 35 and 65

Within four standard deviation: 50 ± 5(4) or between 30 and 70

Thus, if you were to be asked for a number that is between 1 and 2 standard deviations from the mean, both 42 and 58 would be acceptable answers.