Measures of Central Tendency
Mean, Median & Mode Activity
Click on the website below to learn about mean, median, mode, and range as well as try some examples.
Worksheets
The three kinds of averages students will encounter are mean, median, and mode. The 3 M’s (as they will be referred to here) describe a typical item is a set of data. The 3 M’s are referred to as measures of central tendency because they tell us that something is central or common to the particular data set we are looking at. The difficulty that can arise comes from the fact that all three measures can be extremely different for the same data set.
First off the mean, which of the three is the most difficult to understand is usually taught first (see most textbooks and refer to the state performance indicators not that this how it should be introduced but that is a story for a different day). When we discuss mean, we are usually talking about the arithmetic mean or average. Most students know that to calculate the mean, you add up the numbers in a data set and then divide by the number of items in that set.
There are two ways to think about the mean. One idea that should be developed is the idea of mean as the balance point on a scale. The other focuses on the idea of equal distribution. Students need to see that for any data set the sum of the amounts above the mean is always equal to the sum of the amounts below the mean. Also you can look at it as the sum below the mean must balance with the sum above the mean.
Discussion of mean, without using the term, can begin in the primary grades. Students can represent the number of letters in their first name with connecting cubes. They could then try to even them out by switching blocks to even off the individual trains. If there is an uneven number, for example there are a majority of names with 6 letters and some with 7 letters; younger students could express the mean as being between 6 ands 7 letters. Older students would apply the algorithm and find out the exact number with a fraction or decimal representation.
Median is the middle number in a set of data when the numbers are placed in order (least to greatest or greatest to least). If there is an even number of numbers, then the two middle numbers are averaged. Median is used best when there are few high and low values in the data set. Selling prices of a house is a good example of when median is used. A few extremely expensive houses in a certain area will distort the mean value of the homes. The expensive home prices will not distort the median to the extent it would the mean.
Mode is the number or numbers that appear most often. If there is no number that appears most often then there is no mode. If there are two numbers that appear most often, the data set is considered bimodal. If there are three or more values that appear the same number of times, there is no mode. Mode is a good indicator to use when you are trying to determine the most popular “something.” For example, if an ice cream store sold the most chocolate chip ice cream cones and vanilla cones, it would be beneficial to use mode as compared to median or mean because that would let the owner know that he/she need to reorder more chocolate chip and vanilla as compared to a flavor that did not sell as well.
