Table of Contents
Mean
The mean is the arithmetic average of a set of numbers. To find the mean you simply sum all of the numbers together and divide by the # of numbers in the set.
Example
What is the average of 80, 90, 90, 100, 85, and 90?
Median
The median is the number in the middle. To find the median, order the numbers in a set from lowest to highest, then find the number that is exactly in the middle. If there are an even # of numbers, then average the two numbers in the middle to find the median.
Example
What is the median of 80, 90, 90, 100, 85, 90?
Rearrange the set above from lowest to highest
80 85 90 90 90 100
Since there’s an even number of numbers, take the average of the two numbers in the middle: 90 and 90. The median of the set is 90.
Mode
The mode is the value that occurs the most frequently. To find the mode begin by ordering the numbers from lowest to highest. Look for the number that occurs most often. A set of numbers can have more than one mode.
Example
What is the mode of 80, 90, 90, 100, 85, 90.
In the set of numbers above, the mode is 90, since 90 appears 3 times.
Range
The range is the difference between the highest and lowest value. The range tells us how far data is spread out.
Example
What is the range of the 80, 90, 90, 100, 85, 90.
To find the range, subtract 100 (the highest value) from 80 (the lowest value). 100 – 80 = 20, so the range is 20
Standard Deviation
Standard deviation describes how spread out your data is. Computation of standard deviation can be a bit complex and is outside the scope of what the GMAT tests. However, the GMAT will often test the concept of standard deviation, so test takers must have at least a rudimentary understanding of this concept.
One conceptual way to think about the standard deviation is that it is a measure of data spread. If we had several data points and plotted them in histogram format (plotting the count of how often a number occurs), we might get a curve with the shape below. The figure shown below is a bell shaped curve with a standard deviation of 1. Notice how tightly concentrated the distribution is.
The second figure below is a different bell shaped curve, one with a standard deviation of 2. Notice that the curve is wider, which implies that the data is less concentrated and more spread out.
Finally, a bell shaped curve with a standard deviation of 3 appears below. This curve shows the most spread.
Numerically, the standard deviation represents the distance of each individual data point from the average of all the data points.
Essential Standard Deviation Facts:
- Adding a constant to all numbers in a set does not change the standard deviation
- Numbers that are tightly clustered around an average have a smaller standard deviation than numbers that are spread out
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