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Introduction to Statistics: Mean, Median, and Mode
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Abstract

The goal of this lesson is to introduce the concepts of mean, median and mode and to develop understanding and familiarity with these ideas. The Measures Activity lets students explore mean and median in an efficient way; the Mean, Median and Mode Discussion helps them to formalize their knowledge.

Objectives

Upon completion of this lesson, students will:

  • understand three different measures of "center"
  • have been exposed to multiple ways of expressing a set of numbers
  • have practiced their arithmetic skills

Standards Addressed:

Textbooks Aligned:

Student Prerequisites

  • Arithmetic:Students should understand:
    • sums, differences, and quotients for all activities.
  • Technological::
    • Each student or group of students working together will need a computer with a web browser. Students should be comfortable using the computer and browser. Calculators may be helpful for solving problems that arise in discussions.

Teacher Preparation

Key Terms

arithmetic meanSee mean
averageIt is better to avoid this sometimes vague term. It usually refers to the (arithmetic) mean, but it can also signify the median, the mode, the geometric mean, and weighted mean, among other things
histogramA bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval
meanThe sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean
median"Middle value" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50%
modeFor lists, the mode is the most common (frequent) value. A list can have more than one mode. For histograms, a mode is a relative maximum ("bump"). A data set has no mode when all the numbers appear in the data with the same frequency. A data set has multiple modes when two or more values appear with the same frequency.
multimodal distributionA distribution with more than one mode. The histogram of a multimodal distribution has more than one "bump"
rangeThe range of a set of numbers is the largest value in the set minus the smallest value in the set. Note that the range is a single number, not many numbers
totalA total is determining the overall sum of numbers or a quantity.

Lesson Outline

  1. Focus and Review

    Remind students of what they have learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

    • Does anyone know what "average" means?

  2. Objectives

    Let the students know what they will be doing and learning today. Say something like this:

    • Today, class, we are going to learn about mean, median, and mode.
    • We are going to use the computers to learn about mean,median, and mode, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

  3. Teacher Input

    • Lead a discussion, or the instructor can prepare a "live" discussion, to deepen and formalize the students' intuitive understanding of mean, median, and mode. (10-20 min)

  4. Guided Practice

    • Introduce and develop the concepts of mean and median with the Measures activity. Students will change parameters and discover patterns related to mean and median. Students can choose their own focus of measure, their own quantity, and their own units. (20 min)

  5. Independent Practice

  6. Closure

    • You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outline

  • Combine this lesson with the Bell Curve Lesson for a look at how means are tied to distributions

Suggested Follow-Up

This lesson introduced the students to some basic ways of describing sets of data. The next lesson, Histograms and Bar Graphs, introduces histograms, bar graphs, and the concept of class interval. Students will learn to distinguish between bar graphs and histograms and to use each in the appropriate situations.

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