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Making Meaning out of Mean, Median, & Mode

Students often are asked to calculate mean, median, and mode in school. But what do these statistics mean? Here is a fun sticky note activity to help students understand.

For starters, here are the basic definitions.

Mean: Add the data and divide by the number of data items.

Median: Middle number (if even # of of items, find the mean of the two in the middle).

Mode: Data item that occurs the most often (there may be none or more than one).

Ask children, "What is your favorite kind of cereal?" Then say, "Let's look at the amount of sugar in the top grocery shelf of cereals." Together, make a sticky note graph on the kitchen table or poster board like the picture below. Use the following numbers.

0 grams-4 cereals

1 gram-1 cereal

2 grams-2 cereals

3 grams-5 cereals

6 grams-3 cereals

10 grams-2 cereals

11 grams-3 cereals

Find the mode by looking for the tallest bar (3 grams).

Find the median by having the child touch sticky notes from one end, and you work from the other end towards the middle (3 grams).

Find the mean by adding all the data (91 grams), and dividing by 20 because there are 20 sticky notes (4.55 grams). Use a calculator as this task is not about learning to divide.

Play the "What If?" game. Ask questions like the ones below, and predict the answers by moving sticky notes. Then touch sticky notes from the ends to the middle to find the median, and calculate to find the mean.

Suppose you remove the three cereals with 6 grams of sugar per serving and add three new cereals, each with 9 grams of sugar per serving. How do the mean and median change? Why?

Using the new distribution, what happens to the mean and median if you remove a cereal with 3 grams of sugar and add a cereal with 8 grams of sugar?

What if you do that again?

And again?

Make up your own What-If questions.

How does replacing smaller data values with larger data values affect the mean and the median?

This short sticky note activity helps students grasp not just what the mean, median, and mode mean, but how they are affected by slight changes in the data, deepening their understanding of these statistics. Top it off by snacking on cereal!

Source: Connected Mathematics2 Grade Seven by Lappan, Fey, Fitzgerald, Friel & Phillips (2009) Data Distributions 2.4.

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