Mean, Median, and Mode Study Guide (page 2)

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Updated on Oct 4, 2011


The mode of a group of numbers is the number that appears most often.

Example: Find the mode the most common classroom size, at the Chancellor School.

Solution: Scanning the data reveals that there are more classrooms with 15 students than any other size, making 15 the mode:

11 16 16 17 18 30

Had there also been three classrooms of, say, 16 students, the data would be bimodal—both 15 and 16 are the modes for this group:

11 17 18 30

On the other hand, had there been an equal number of classrooms of each size, the group would NOT have a mode—no classroom size appears more frequently than any other:

11 11 13 13 15 15 17 17 19 19

Hook: Here's an easy way to remember the definitions of median and mode.
  Median: Picture a divided highway with a median running right down the middle of the road.
  Mode: The MOde is the MOst popular member of the group.


Use these tricks to remember what each term means:

Mean: That mean teacher gave me a failing average!
Median: "Median" sounds like medium, which is the size in the middle of small, medium, large. So "median" is the number in the middle.  
Mode: "Mode" sounds the closest to "most," so the mode is the number(s) that occurs the most.

Average Shortcut

If there's an even-spacing pattern in the group of numbers being averaged, you can determine the average without doing any arithmetic! For example, the following group of numbers has an even-spacing "3" pattern: Each number is 3 greater than the previous number:

6 9 12 15 21 24 27 30

The average is 18, the number in the middle. When there is an even number of evenly spaced numbers in the group, there are two middle numbers, and the average is halfway between them:

6 9 12 15 24 27 30 33

This shortcut works even if each number appears more than once in the group, as long as each number appears the same number of times, for example:

10 10 10 20 20 20 30 30 40 40 40 50 50 50

You could have used this method to figure out sample question 1. Order Barbara's grades from low to high to see that they form an evenly spaced "2" pattern:

88 90 92 94 96 98 100

Thus, Barbara's average grade is the number in the middle, 94.

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