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The GMAT tests some of the basic concepts of statistics, including mean, median, and range, as well as more challenging concepts such as standard deviation (SD).
Skipping the standard deviation formula
Fortunately, you will not need to actually calculate the standard deviation of a set—you will merely need to understand what standard deviation is and how it is calculated.
Unless you simply want to learn the formula for calculating SD, you do not need to spend time doing so in preparation for the GMAT. However, you should be comfortable with the concepts relating to it and how they work together.
Dispersion
Standard deviation measures the dispersion of the values within a set. This means, in nontechnical terms, “how spread out they are.” For example, the set {2, 4, 6} has the same SD as the set {8, 10, 12}; each term in the first set is the same distance from the mean, or average, of that set as each term in the second set. But {1, 3, 5} and {3, 6, 9} have different SDs, because the terms are more “spread out” in the second set. The second set has a with a wider spread, or dispersion, therefore it has a higher SD than the first one.
When standard deviation shows up on the GMAT, it tends to appear in Data Sufficiency questions. This makes sense, because these questions test your knowledge of whether you have enough information to get to a solution—not your ability to actually solve a problem. Plus there are conditions of sufficiency required to be able to determine the SD of a set.
At least one of these pieces of information is required to have sufficiency for determining a set’s SD:
- The value of each term in the set
- The distance from the mean of each term in the set
- The variance of the set
In other words, if you know all of the terms, you can determine the mean and the SD. If you know the mean and the distance from the mean of each term, you can then find the SD. I’ll explain variance later; right now, let’s look at these two points.
Mean vs. median
Standard deviation concerns the mean (average), not the median (middle term), of a set of numbers. Although in some sets the mean and median is the same, unless you know this to be true, simply knowing the median of a set does not allow you to determine the SD. (In fact, simply knowing the mean of a set is also insufficient. You must know the distance from the mean of each term, not just the mean.)
GMAT Data Sufficiency questions pertaining to SD may include the median of the set in one of the statements. This is intended to catch novice test-takers off guard; don’t be fooled by these easy to confuse terms. The mean is the average, and the median is the middle number. The median of a set plays no role in its SD unless the median equals the mean.
Uniform changes to sets
Another way the GMAT may test your understanding of standard deviation is through manipulating the terms in the set. Adding or subtracting the same value from all terms does not change the SD. For example, {1, 2, 3, 4, 5} and {3, 4, 5, 6, 7} have the same SD: The difference from the mean doesn’t change just because all of the terms increased by 2. The distance between the numbers stays the same. Likewise, {a, b, c} and {a+1, b+1, c+1} have the same SD.
Multiplying the terms in the set does change the SD. The set {1, 2, 3} has a smaller SD than the set {2, 4, 6}. Multiplying the terms increases their dispersion and thus their SD. Raising the terms to an exponential power is a type of multiplication and also increases a set’s SD; 
and 
do not have the same SD.
Variance
The steps in the formula for standard deviation include squaring the distances from the mean of all terms, summing those squares, and then finding the average of that sum. This average is called the variance, and if you know a set’s variance, you simply take the square root to find the SD. A Data Sufficiency question may include the variance, so recognizing its relationship to the SD is important.
So don’t worry much about SD on the GMAT. This basic overview is really all you need to understand to be able to tackle any such questions on Test Day.
Looking to get some hands-on experience with statistics on the GMAT? Take a free online practice test to check your Quant skills.
The post Land Your Score: Standard Deviation on the GMAT appeared first on Business School Insider.
