1 MATB344 Applied Statistics Chapter 1 Describing Data with Graphs.
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Chapter 1
Section 5 – pg 35
Graphs in Science
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The Importance of Graphs
• Creating a data table is one way to organize experimental data
– Graph: a “picture” of your data
• Can reveal patterns or trends that words and data tables cannot
• The three types of graphs that scientists commonly use are bar graphs, circle
graphs, and line graphs
Pg 35
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Why are Line Graphs Useful?
• Line graphs are used to display data to show how one variable (the responding variable) changes in response to another variable (the manipulated variable)
Pg 35
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Plotting a Line Graph
• When should you plot a line graph? – When your manipulated variable is continuous (there are
possible points between what you tested)
• Step 1: Draw the axes – Horizontal axis (x-axis) runs left to right – Vertical axis (y-axis) runs up and down
• Step 2: Label the axes – Label horizontal axis with name of manipulated variable – Label vertical axis with name of responding variable
• Make sure you include the units of measurement (ie ft, $, %)
• Step 3: Create a scale – Origin: the point where the two axes cross – Coordinate: a pair of numbers used to determine the
position of a point on a graph
Pg 36
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• Step 4: Plot the data
– Data Point: the point showing the location of the intersection between the x and y coordinates
• Step 5: Draw a “line of best fit”
– Line of Best Fit: a smooth line that reflects the general pattern of a graph
– Linear Graph: a line graph in which the data points yield a straight line
• Step 6: Add a title
– The title should identify the variables or relationship shown in the graph
Pg 36
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Why Draw a Line of Best Fit?
• A line of best fit emphasizes the overall trend shown by all the data taken as a whole
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Slope
• Slope: the steepness of the graph line
• The slope of a graph line tells you how much y changes for every change in x
– How much the responsive variable is changing in response to the manipulated variable
• Slope = rise/run
Pg 39
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Using Graphs to Identify Trends
• Nonlinear graph: a line graph in which the data points do not fall along a straight line
• Line graphs are powerful tools in science because they allow you to identify trends and make predictions
Pg 40
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Linear Trends • When a graph is linear, you can easily see how two
variables are related
• It is also easy to predict points not on your line
Pg 40
In this graph what would y be if x is 5?
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Nonlinear Trends
• Nonlinear trends show different trends
• Because each of these graphs reveals a trend in the data, they are useful in understanding how the variables are related
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No Trend
• In other nonlinear graphs, the data points may be scattered about in no recognizable pattern
– This means there is no relationship between the two variables
Pg 41
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Chapter 1 Section 5 Homework – pg 41
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1A. What can graphs reveal that data tables cannot?
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1B. What can a line graph tell you about the relationship between the variables in an experiment?
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1C. Could you use a line graph to show data about how body mass (the
responding variable) changes with height (the manipulated variable)?
Explain.
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2A. What is a line of best fit?
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2B. What does calculating the slope of a graph line tell you about the data?
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2C. How does a graph line with a steeper slope compare to one with
a shallower slope?
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3A. List two things that line graphs allow scientists to do.
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3B. Describe how Graphs A and D in Figure 24 differ.