Graphing
Graphing
• Representing numerical information in a picture.
• Graph shows a picture of a relationship -how two processes relate
-what happens when two events occur simultaneously
-how one factor influences another
Parts of a Graph• Factors plotted along
an axis• Numeric or some
measurable term• Uses a scale• Horizontal = x-axis =
abscissa• Vertical = y-axis =
ordinate
• Independent variable on x-axis (horizontal)•Variable that you select to study•Variable that you manipulate
• Dependent variable on y-axis (vertical)• Values that are
produced• Variable that responds
Data Table – data collected is organized in a table.
Independent Variable → Goes on X axis →data on left side of data table
Dependent Variable → Goes on Y axis → data on right side of data table
Color ofm&m’s
% of each color
Brown 13Yellow 14Red 13Blue 24
Orange 20Green 16
Types of Graphs
Bar Graphs - used to compare
amounts of the same type of measurement
Blazer Liberty Durango Escape Honda0
5
10
15
20
25
City Mileage for Gas Consumption
Type of Car
Num
ber o
f mile
s
Monthly BudgetPie Graph
-used to represent percentage data
Line Graphs-used for representing data that constantly changes at regular intervals- may not necessarily show a regular pattern
Using a graph to determine information not directly measured
or calculated.
• Done with line graphs• Is impossible to measure every point that
exists on that line or a distance from either end of the line constructed from the experimental points.
• Use the processes of interpolation and/or extrapolation
• Interpolation –
• The process of obtaining a value from a graph or table that is located between data points plotted or major points given.
• You make a prediction about what would
happen at a given point.
• How much money did the student earn after 5 hours?
• Since you know how the experiment worked before and after the point of interest, you have a better chance of making a correct prediction.
• Extrapolation – • The process of obtaining a value from a chart or
graph that extends beyond the given data.
• The “trend” of the data is extended past the last point given and an estimate is made of the value.
• You can predict what would happen beyond the measured data.
• Must be done with caution. You must assume that any variable in the experiment would not greatly change.
• How much money did the student earn after 10 hours?
• Extrapolation may not be very accurate since you are assuming the trend continues outside the boundaries of your data points
Analyzing a GraphRelationship is
Inversely Proportional (one
value increase and the other
decreases – line is a curve)
Relationship is Directly
Proportional (both values increase or
decrease at the same rate – line is
straight)
Line Graphs – Kinds of Relationships
Classroom Exercise 1:
Relationship – steady increase over a period of time
Curve is a straight line ~ since both factors are increasing the relationship is directly proportional
Relationship – increases over period of time until a max is reached and then decreases
Relationship – change over period of time then remains constant
Relationship – no change
Relationship – decrease over a period of time
Relationship – unchanged, decrease, remains constant
Building a Graph
1. Identify the variables2. Determine the range of each variable3. Determine the scale (fill at least 2/3 of
paper)4. Number and label each axis5. Plot the data points6. Draw the graph7. Title the graph (provide a key if needed)
“Connecting the dots”
• A line of best fit or also called a “best fit line” is a straight line that best represents the data on a scatter plot.
• This line may pass through some of the points, none of the points, or all of the points.
• It may also be called a "trend" line.
KEY
Best Fit Line
Best fit line may not go through the “O” point
• Choose two points that you think will form the line of best fit.
Classroom Exercise 2:
Draw a graph for this data
Time(min)
Temperature(ºC)
0 10.5 11.0 21.5 112.0 232.5 363.0 463.5 534.0 604.5 725.0 786.0 887.0 1008.0 100
Classroom Exercise 3:
Building a Bar Graph
Month Precipitation in Inches
January 0.78February 0.96
March 2.03April 3.10May 4.29June 4.02July 3.85
August 3.26September 2.91
October 2.31November 1.76December 1.10
Classroom Exercise 4:Building a Circle Graph
Type of tree
Number found
Percentage of total
Angle for pie section
Oak 539
Maple 758
Beech 319
Birch 1327
Hickory 222
Total 3165 100% 360⁰
Classroom Exercise 5:Interpolation and Extrapolation of Data
Time (s)0 1 2 3 4 5 6 7 9
0
10
20
30
40
50
60
70
80Velocity as a Function of Time
Classroom Exercise 6:Interpreting a Graph
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