Overview

The class makes a table and scatter plot of all students’ arm spans vs. heights. Students then investigate the effect of outliers on central tendency and find the line of best fit using medians (or median fit line).

Objective

Students will create a scatter plot and find the line of best fit of the data.

Standards Address

Mathematics — Data Analysis

Grade 8

Data Collection, Benchmark A

01. Use, create and interpret scatter plots and other types of graphs as appropriate.

Statistical Methods, Benchmark C

05. Explain the mean’s sensitivity to extremes and its use in comparison with the median and mode.

Statistical Methods, Benchmark F

06. Make conjectures about possible relationship in a scatter plot and approximate line of best fit.

 

Materials

• Tape measures

• Rulers

• Graph paper

Procedure

Day 1:

1. Divide students into pairs. Each student will use a tape measure to measure the other’s height and arm span. You may want to demonstrate how the students should conduct the measurement.

2. On the board draw a table, with the first entry being your height and your arm span as an ordered pair. As the groups finish, they will add their measurements to the table. Have students recall that a “regular” polygon has the same height as width. If their own height and arm span are equal, they would be considered “regular.”

3. When all students’ numbers are recorded on the board, begin drawing a large scatter plot. Each student will come up front and plot his or her own point where it belongs. As the students add their numbers, discuss the following:

How do you know where to plot the point?

What do the x-axis and y-axis represent?

What intervals should we use for our graph?

Discuss labels and title for the graph. How does each point being plotted

relate to the table?

4. Option: Have students make their own scatter plot using the graph paper on p. 162.

5. Have the students rewrite their measurements as ordered pairs as they come up.

6. The pairs of students should also draw the scatter plot on their own graph paper. This way, they will have the information for the next part of the lesson.

7. Have the students complete the Day 1 handout with their partners.

Day 2:

1. Discuss the results of the central tendency and the positive correlation of the data. Discuss the effect of any outliers on the mean. Students should understand that this is the reason they will use the median in the next step, as opposed to the mean or mode.

2. Instruct the students to follow these steps for creating the line of best fit: (Download a PDF file of the following steps)

Count the total number of points and divide by three. Draw two vertical dashed lines so there are approximately the same number of points in each of the three sections. The two outer sections should have the same number of points, if possible. Notice where the two occurs, there are two identical points. The following example uses 13 points, so the graph is divided into 4-5-4 points.



Now use a ruler to find the middle horizontally among the four points on the left (between the second and third point). Draw a small vertical line. Then find the middle vertically among the four points on the left. Draw a small horizontal line.



Do the same with each section.



Use a ruler and try to line up the three x’s you have drawn. If the x’s lie approximately on a straight line, connect the first and last x with your ruler and then slide the rule one-third of the way to the middle x. Draw the line.



3. Guide students through this process with the first day’s data. The data should yield a strong positive correlation, but you can discuss the effect of outliers with them.

4. Have students complete the Day 2 student handout with their partner.

Evaluation:

Category	4	3	2	1
Scatter Plot Construction	Student constructed the scatter plot correctly and paid attention to scale, labels, etc.	Student constructed the scatter plot correctly but missed attention to details.	Scatter plot had mistakes or unclear scale; there is minimal attention to detail.	Student does not understand scatter plot construction or how to form the scale.
Central Tendency	Student correctly calculated all three measures of central tendency and understood the change to the mean with an outlier present.	Student calculated the scatter plot correctly but misinterpreted change to the mean, or student made an error in calculation.	Student made a significant error in calculation and does not understand effect of outliers on mean.	Student does not understand how to calculate measures of central tendency and does not understand outliers effect on mean.
Line of Best Fit	Student correctly constructs line of best fit and is able to interpolate correctly.	Student made a minor error in line of best fit, but understands the process.	Student made an error in line of best fit and is not able to interpolate correctly.	Student does not understand how to find line of best fit and cannot interpolate correctly with the line.
Concepts	Student has a clear understanding of scatter plots and line of best fit and has communicated that effectively.	Student has satisfactory understanding of the major concepts, but has small misunderstandings.	Student has major misunderstandings of the concepts and cannot complete work on his own.	Student does not display understanding of the major concepts or did not complete the assignment.