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. The middle number (the 4th one in the list) is 11. So, the median is 11.
Example 2:
Find the median of the set {2, 5, 5, 6, 8, 8, 9, 11}.
There are 8 numbers in the set -- an even number. So, find the average of the middle two numbers, 6 and 8.
So, the median is 7.
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.
