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Mean, Median, Mode

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Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you 're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

The "range" is just the difference …show more content…

So if you 're not certain how you should answer the "mode" part of the above example, ask your instructor before the next test.

About the only hard part of finding the mean, median, and mode is keeping straight which "average" is which. Just remember the following:

mean: regular meaning of "average" median: middle value mode: most often

(In the above, I 've used the term "average" rather casually. The technical definition of "average" is the arithmetic mean: adding up the values and then dividing by the number of values. Since you 're probably more familiar with the concept of "average" than with "measure of central tendency", I used the more comfortable term.)

A student has gotten the following grades on his tests: 87, 95, 76, and 88. He wants an 85 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?
The unknown score is "x". Then the desired average is:

(87 + 95 + 76 + 88 + x) ÷ 5 = 85

Multiplying through by 5 and simplifying, I get:
87 + 95 + 76 + 88 + x = 425 346 + x = 425 x = 79

He needs to get at least a 79 on the last test.

You can use the Mathway widget below to practice "Data Measurement and Statistics", subtopic "Finding the Median". Try the entered exercise, use the "Select Topic" menu to practice modes and means, or type in your own exercise. Then

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