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There are multiple measures of center:
The mean is the default measurement that you should use if there's no compelling reason to use anything else.
The mean is the best measurement to use if possible because it's the most versatile measure of center and therefore, the most appropriate one in the vast majority of cases. However, there are certain situations in which the mean is not an appropriate gauge for center. In those cases, you should use the median. You will rarely use the mode.
Sometimes the mean is a poor representation of where the center really is, so the median becomes a better measure of center.
Consider this table of one company’s employees and their salaries:
| Title | Number of Employees | Salary |
|---|---|---|
| Boss | 1 | $200,000 |
| Manager | 3 | $55,000 |
| Shift Worker | 8 | $42,000 |
The mean of this set of data is about $58,000, but how many of the employees actually make more than $58,000 and how many make less than $58,000?
Eleven of the 12 people make less than $58,000. Only one employee makes more than that, and that employee makes substantially more. The boss’s $200,000 salary is an outlier. Therefore, the mean doesn’t make very much sense as a measurement of the middle.
In this case, a better measure of center would be the median. If you took all the salaries and wrote them out from least to greatest, the median (the one in the middle) would be $42,000. That more accurately describes what a typical worker makes.
$42,000
$42,000
$42,000
$42,000
$42,000
$42,000
$42,000
$42,000
$55,000
$55,000
$55,000
$200,000
When should you use mode? The mode isn’t used very often. It's used mainly for qualitative data sets, to determine the category that has the most values in it. Consider the graph below:
In this case, the mode is biology, the red section.
The mode is also used to describe the peak of a distribution, such as in a histogram.
Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.
