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Line & Scatter
(What Would You Use: Part 2)

By: Brink Harrison


Time: One class period
Preparation Time: 5-10 min making overheads
Materials: Scatter plot Overhead
Line Graphs overhead
Homework
Teacher Background

Abstract
Discussing line graphs and scatter plots allow students to better understand the types of data represented by the respective graphs and how these graphs can be used to interpret trends. Students review the structures of line graphs and scatter plots, specifically possible relationships between the variables on the graphs. Students will decide whether a scatterplot or line graph is the appropriate form of display when they create the graphs for their final project on arsenic in a given community.


Objectives

Students will be able to:

i. Determine the type of correlation, if one exists, between the variables on a scatterplot
ii. Construct a scatterplot from a given set of data
iii. Construct a line graph from a given set of data

Math Standards
Data Analysis and Probability
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Measurement
Understand measurable attributes of objects and the units, systems, and processes of measurement


Teacher Background
See attached sheets

Related and Resource Websites
http://nces.ed.gov/nceskids/graphing/
http://www.statcan.ca/english/edu/power/ch9/scattergraphs/scatter.htm
http://noppa5.pc.helsinki.fi/koe/flash/corr/ch16.html

 

Activity
1. Review the homework from the lesson on bar graphs and histograms. Allow the students, time to discuss the differences they find in their work.

2. Tell them, “We will come back to bar graphs and histograms later, but today we are going to look at two more types of graphs: the line graph and the scatterplot. How are these two types of graphs similar? How are they different?” Allow time for students to discuss the similarities and differences.

3. Hopefully somebody will mention that both line graphs and scatter plots compare two variables. Each variable is plotted along an axis. The independent variable lies on the horizontal axis and the dependent variable lies on the vertical axis. Both require that you pick a value for the independent variable and then plot a point at the corresponding value of the dependent variable. The big difference is that, in a line graph, the consecutive points are connected by a line segment while the points in a scatter plot are not connected at all.

4. Put up the first page of the scatter plot overhead and discuss how it is made. Point out that the pattern of the data points on the scatter plot reveals the relationship between the variables. Scatter plots can illustrate various patterns and relationships, such as:

• data correlation (the trend you see with the points)

• positive correlation between variables (2nd page of overhead)

• negative correlation between variables (2nd page of overhead)

• scattered data points - zero correlation between variables (3rd page of overhead)

• spread of data -zero correlation between variables (4th page of overhead)

• outliers (5th page of overhead)

Adapted from: http://www.statcan.ca/english/edu/power/ch9/scattergraphs/scatter.htm

The spread of data and outliers are optional, but it is vital that the students have a good understanding of positive, negative, and zero correlation. Another good website that uses animation and allows you to change the value of correlation between variables is:
http://noppa5.pc.helsinki.fi/koe/flash/corr/ch16.html

5. Put up the first page of the Line Graph overhead (the U.S. Public School Student Membership from: http://nces.ed.gov/nceskids/Graphing/line.asp ) Discuss how the graph is made, and its similarities in terms of structure to scatter plots. Line graphs are like scatter plots in that they record individual data values as marks on the graph. The difference is that a line is created connecting each data point together. Line graphs are able to show relationships more clearly than scatter plots do.

6. Have the students answer the questions.

7. Put up the 2nd page of the Line Graph overhead (the Red River Discharge Rate graph from: http://www.ncsu.edu/labwrite/res/gh/gh-linegraph.html ) Discuss with the students how an overall trend is shown on the line graph, but that local trends, or local changes, between individuals can also be seen. These local changes from point to point can be seen as the line graph shows a change in direction

8. Ask the students, “What does it mean if the graph goes up as we move to the right between consecutive points? What does it mean if the graph goes down to the right between consecutive points? Why might a business think that it is important to be able to see the local change between any two pairs of points on the graph?”

9. Have the students answer the questions.

The Red River Discharge Rate graph demonstrates that, unlike scatter plots, the independent variable can be either scalar or ordinal. In the graph, the variable on the x-axis, “Month”, could be thought of as either scalar or ordinal. The data represented on the Red River Discharge Rate graph could have also been produced as a bar graph. However, you would use a line graph when you want to be able to more clearly see the rate of change (slope) between individual data points. If you only wanted to know the discharge rate for the individual months, you would almost certainly use a bar graph instead of a line graph.

10. Put up the third page of the Line Graph overhead (the multiple year Red River Discharge Rate graph from http://www.ncsu.edu/labwrite/res/gh/gh-linegraph.html )

11. Stress the need for a coding scheme. Tell the students, “Since there is more than one independent variable, some sort of coding is needed to indicate which year each line is. Though we could label each line with text indicating the year, it is more efficient to use color and/or a different symbol on the data points. We will need a legend to explain the coding scheme.” Have the students answer the questions.

12. After students have answered the questions review that in summary, line graphs:

• show specific values of data well

• reveal trends and relationships between data

• compare trends in different groups of the independent variable

http://www.statcan.ca/english/edu/power/ch9/linegraph/line.htm

If your students are uncertain about how to make a line graph on paper, the website
http://www.howe.k12.ok.us/~jimaskew/.htm gives very clear instructions.


Homework

Have the students do problems 1 and 2 on the attached homework sheet.

Embedded Assessment

You can assess the students understanding of scatter plots and the correlation between variables by using informal discussions while looking at the overheads for the scatterplots. As students answer the questions on the Line Graph overheads, they will be self-assessing their ability to interpret the graphs. At the same time, the informal discussions that will accompany their responses will provide the opportunity for you to assess their understanding as well.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


PULSE is a project of the Community Outreach and Education Program of the Southwest Environmental Health Sciences Center and is funded by:


an
NIH/NCRR award #16260-01A1
The Community Outreach and Education Program is part of the Southwest Environmental Health Sciences Center: an NIEHS Award

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Supported by NIEHS grant # ES06694


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