In a set of numbers, it is often useful to find, as close as is possible, one number to describe the center of the data. One number is never going to perfectly describe the data. The mean, the median, and the mode are three statistics that attempt to describe the center of a set of data.
...most commonly referred to as the "average."
The mean is found by adding up all the numbers in a data set and dividing by the number of numbers.
Points scored in the past 5 games: 15 14 15 11 10
Find the mean: Add the scores 15 + 14 + 15 + 11 + 10 = 65 Divide by 5 (the number of games ) 65 ÷ 5 = 13 The mean is 13.
The mean can be thought of as a fair share. It represents what would happen if the data were "evened out" as best as possible. In the example above, if the 65 total points that were scored in the five games were scored evenly in the five games, each game would have had a total of 13 points.
...the middle of a sorted list of data. It separates the lower half of the data from the upper half of the data.
The median is found by arranging the data from least to greatest and finding the middle number. If there is an even number of data points, there will be two numbers in the "middle." The mean of those two numbers is the median of the set. Add the two middle numbers and divide the sum by 2.
Points scored in the past 5 games: 15 14 15 11 10
Find the median: arrange the numbers from least to greatest 10 11 14 15 15
The median is the number in the middle. The median is 14.
With an even number of data points:
Points scored in the past 6 games: 15 14 15 11 10 16
Find the median: arrange the numbers from least to greatest 10 11 14 15 15 16
Both 14 and 15 are in the "middle" of this data set. Find the mean of these two numbers.
14 + 15 = 29 29 ÷ 2 = 14.5 The median is 14.5
...the number that occurs most often in a set of data.
Find the mode by noticing which number in the set of data, if any, occurs more often than any other numbers.
If no number occurs more than once, there is No Mode.
If there are several numbers that occur an equal number of times, there can be several modes. A set of data may be bimodal, or trimodal....
Points scored in the past 5 games: 15 14 15 11 10
Find the mode, the number that occurs most often: 15 14 15 11 10
The number 15 occurs more than any other number in the data set. The mode is 15.
The mean, median, and mode are measures of center. The range measures how spread out the data is.
The range is the difference between the smallest and the largest numbers in the data set.
Subtract the smallest number from the largest number.
Points scored in the past 5 games: 15 14 15 11 10
Find the range: 15 - 10 = 5 The range is 5.
Besides knowing how to find the different statistics, it is often useful to think about what would happen to the mean, median, or mode if, for instance, an additional number is added to the data set.
For example:
Points scored in the past 5 games: 15 14 15 11 10
How would the mean, median, mode, and range change if 20 points scored in the 6th game?