Mean, Median, and Mode

The Mean of a Data Set

The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.

Example:

Find the mean of the set {2, 5, 5, 6, 8, 8, 9, 11}.

There are 8 numbers in the set. Add them all, and then divide by 8.

= 6.75

So, the mean is 6.75.

The Median of a Data Set

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

Example 1:

Find the median of the set {2, 5, 8, 11, 16, 21, 30}.

There are 7 numbers in the set, and they are arranged in ascending order.  The middle number (the 4th one in the list) is 11.  So, the median is 11.

Example 2:

Find the median of the set {3, 10, 36, 255, 79, 24, 5, 8}.

First, arrange the numbers in ascending order.

{3, 5, 8, 10, 24, 36, 79, 255}

There are 8 numbers in the set -- an even number. So, find the average of the middle two numbers, 10 and 24.

(10 + 24)/2 = 34/2 = 17

So, the median is 17.

The Mode of a Data Set

The mode of a set of numbers is the number which occurs most often.

Example 1:

Find the mode of the set {2, 3, 5, 5, 7, 9, 9, 9, 10, 12}.

2, 3, 7, 10 and 12 each occur once.

5 occurs twice and 9 occurs three times.

So, 9 is the mode.

Example 2 :

Find the mode of the set {2, 5, 5, 6, 8, 8, 9, 11}.

In this case, there are two modes -- 5 and 8 both occur twice, whereas the other numbers only occur once.