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.
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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.
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