Calculating Mean, Median, Mode

We learned how to calculate mean, median, in school, though many of us adults probably forgot how. Our kids and grandkids will eventually learn about mean, median, and mode in school. So we may need to brush up on our averaging skills to help them with their homework when the time comes. Mean, means, and mode are all ways of finding the average, or the measure of central tendency, from a list of numbers; they just go about it in different ways.

Mean

The mean number in the list of numbers is the actual average of those numbers; meaning you add the numbers on the list and divid the sum by the amount of numbers on the list. For example, you have a list of 9 numbers: 13, 18, 13, 14, 13, 16, 14, 21, and 13. Add the numbers:

13 + 18 + 13 + 14 + 13 +16 + 14 + 21 + 13 = 135. Now divide that sum by 9: 135/9 = 15, which is the average of that list of numbers.

Median

When a list of numbers has a range with extremely high or extremely low values, those value extremes can affect the average obtained when using the mean calculations. In those instances it may be more feasible to calculate the average using the median. The median of a list of numbers can be found by putting all the numbers on the list into numerical order and locating the number in the middle of that list.

The middle number on an odd numbered list - like the list of 9 numbers above - is the median. For example, lets use the list of numbers above: 13, 18, 13, 14, 13, 16, 14, 21, and 13. Begin by placing them in numerical order: 13, 13,13, 13, 14, 14, 16, 18, 21. The median number in a list of 9 numbers is the fifth number – counting from either end of the list - which in this case is 14.

If you have an even numbered list (a list with 8 numbers) you add the two numbers in the middle of the list and divide by two. Lets’s take the above list and remove two of the 13s and one of the 14s so that the list reads: 13, 13, 14, 16, 18, 21.. The two numbers in the middle are 14 and 16. Add them together (14 +16 = 30) and divide by 2: 30/2 = 15, the mean of the list.

Mode

With mode, the median number is the number that occurs most often in the list. In this case it may be easier to see the most commonly occuring number if you either place the list in order, or separate the numbers on the list so that you can count them. Let’s go back to list of numbers above: 13, 18, 13, 14, 13, 16, 14, 21, and 13.

List them in order:

13, 13,13, 13, 14, 14, 16, 18, 21.

Or separate the numbers:

13, 13,13, 13

14, 14

16

18

21.

Separating them out, you can clearly see that the number 13 occurs most often in this list, making it the mode.

So for this list of nine numbers, the mean was 15, the median was 14, and the mode was 13. While these numbers are close, you can see that each method will come up with a different result.

Resources

Purple Math. Mean, Median, Mode, and Range.
http://www.purplemath.com/modules/meanmode.htm

Dr. Scott. Ask Dr. Math. Mean, Median, Mode, and Range.

http://mathforum.org/library/drmath/view/58326.html

Algebra Lab. Finding the Mean, Median, and Mode.

http://algebralab.org/lessons/lesson.aspx?file=Algebra_StatMeanMedianMode.xml