The Queen of Mean

The mean is one of those measures of central tendency (along with median, mode and range) that students must learn and use to analyze data. I use a simulation presented as a small group demonstration, to illustrate what the mean is and how it is found.

I start with 5 or six sheets of different colored construction paper spread out on a table. I tell the students that these represent houses. I then use unifix cubes or something similar to represent people/families that live in each house. The cubes that live in a house are all the same color (ie the brown cubes are referred to as the Brown family.) Each house has a different number of people living there.

Then the Queen (sometimes it is me and sometimes I just refer to her) makes a decree that there must be the same number of people living in each house. So people must be moved to fulfill this mean-spirited decree which breaks families apart, and the Queen is dubbed "the Queen of Mean" (I then embellish and repeat this part of the story about how mean she is.)Students can work to figure out how many must be in each house. If they have no clue how to do this, I suggest taking all the people and spreading them around one at a time. (This is the same as adding all of the people together, then dividing by how many houses there are--the steps for finding the mean.) I emphasize several times to put all the people together, then divide them out.

After several simulations with different numbers of people, students get the idea of how to find the mean. I then take the cubes away and ask if they can do it without using cubes. I pose another problem and let them go through the steps of solving it. From this point on, whenever a student doesn't rmember how to find the mean, I say, "Do you remember the Queen of Mean?"

"Oh, yeah!" they respond and I don't have to say anything else.