An Introduction to Mean, Median, and Mode

I. An Introduction to Mean, Median, and Mode

II. Introduction

(1-2 minutes)

The real world offers many situations in which you will want to know some things about a given data set. We will be looking at different data sets and figuring out how to summarize and compare them. We will explore three different key terms - mean, median, and mode. Let's start by looking at some data on raisins.

III. Objective:

· Students will be introduced to the three measures of central tendency - mean, median, and mode.

· Students will begin to see how mean, median, and mode are found.

· Students will gain insight into how these key terms are used in real-life situations.

IV. Lesson

Data Set:

Assume that I gave each one of you a half-ounce box of raisins. If we had the time, I would then ask each one of you to count how many raisins were in your box. Then we would gather this data and form a data set. Assume that this line plot (displayed on the board) represents our results. Each post-it note or x represents a box of raisins and the bottom axes represents the number of raisins in the box.

Questions and Comments:

(»2 minutes)

1. By looking at this line plot or representation of the data, how can you describe it? What can you say about the data?

a. Lead students to notice basic characteristics (i.e. the range, the holes in the data, the most frequently occurring value.)

b. If discussion warrants, discuss outliers.

2. If we were to open another box of raisins, what would be your best guess as to how many raisins the box contains? Why?

a. Students should notice the mode here. If not, lead students to this answer.

b. Give the formal definition for mode - the most frequently occurring data value.

3. What would happen if I was to change the data set? Perhaps, add 5 more boxes of raisins with 37 raisins in them to the data.

(»2 minutes)

4. If I owned the raisin company, and I wanted you to tell me where the data divides in half, what could you say? Why would this be important?

a. Give the formal definition for median - the data value that lies in the middle of the data set; the point with the middle position.

b. Will this point change as more points are added?