Description

What our Using Measures of Center lesson plan includes

Lesson Objectives and Overview: Using Measures of Center teaches students about measures of center and variability and how they are related to the shape of a data distribution. At the end of the lesson, students will be able to relate the choice of measures of center and variability to the shape of the data distribution. This lesson is for students in 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional addition to this lesson is to have your students weigh or measure another object that they all have in common and compare data. You could also have your students measure objects from students in various class periods and compare them.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

USING MEASURES OF CENTER LESSON PLAN CONTENT PAGES

Using Measures of Center

The Using Measures of Center lesson plan includes two content pages. Choosing the correct measure of center (mean or median) and variability (range or interquartile range) is very important when describing a distribution. The shape of the data distribution determines the correct measure of center.

For symmetrical distributions, use the mean to describe the center of the data and the range to describe the variability (spread) of the data. For non-symmetrical distributions, use the median to describe the center of the data and the interquartile range to describe the variability (spread) of the data. Outliers are data points that do not follow the trend of the data. A data set can have more than one outlier!

Data sets with outliers have non-symmetric distributions. Outliers greatly affect the mean and range. However, they do not strongly affect the median or interquartile range.

Examples—With and Without an Outlier

The lesson includes an example that illustrates the effect that an outlier can have on the mean, median, range, and interquartile range.

For the mean, let’s look at an example without an outlier: 4, 5, 2, 2, 4, 3 = 20/6 = 3.33 = 3.5. Next, let’s look the same example with an outlier added: 4, 5, 2, 2, 4, 37 = 54/6 = 9.

Now, let’s look at the median of the same example sets of numbers. First, without the outlier: 2, 2, 3, 4, 4, 5 = 3 or 4. Then, with the outlier: 2, 2, 4, 4, 5, 37 = 4.

For the second set of numbers (the one with the outlier), the mean heavily pulls towards the outlier (the value 37). The mean and median are also very different with an outlier. However, the mean and median are very close together when using the set of numbers without the outlier. Without the outlier, the mean and median are about 0.2 units apart. With the outlier, they are 5 units apart.

Next, let’s find the range using the same sets of numbers as before. First, without the outlier: 4, 5, 2, 2, 4, 3 = 5 – 2 = 3. Next, with the outlier: 4, 5, 2, 2, 4, 37 = 37 – 2 = 35.

Then, let’s find the interquartile range without the outlier: 2, 2, 3, 4, 4, 5 = 4 – 2 = 2. Finally, with the outlier: 2, 2, 4, 4, 5, 37 = 5 – 2 = 3.

The second set of numbers (the one with the outlier) has a much higher range. However, the interquartile range is about the same.

The lesson closes with a reminder that the shape of a distribution determines the correct measure of center (mean or median) and variability (range or interquartile range) for a data set.

USING MEASURES OF CENTER LESSON PLAN WORKSHEETS

The Using Measures of Center lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

LUNCH DATA ACTIVITY WORKSHEET

Students will work in groups to complete the activity worksheet. Each student will weigh their lunch (including the container) and record the results in the table, rounding their measurements to the nearest pound. They will then create a dot plot with the data from their table and calculate the mean, median, mode, and range of their group’s data set. Finally, they will compare and contrast the results of their data with another group by listing one similarity and one difference.

DISTRIBUTION PRACTICE WORKSHEET

For the practice worksheet, students will choose the appropriate measures to describe the center and spread of each distribution shown on the worksheet. They will justify their response based on the shape of the distribution.

MEASURES OF CENTER HOMEWORK ASSIGNMENT

The homework assignment asks students to use the two data sets listed on the worksheet to calculate their measures of center. They will then answer a few questions about the data sets and their measures of center.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the homework assignment. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.