1. Graphing

2. 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

3. 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

4. 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

5. Data Table – data collected is organized in a table.
Color of
m&m’s
% of each color
Brown 13
Yellow 14
Red
Blue 24
Orange 20
Green 16
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

6. Types of Graphs Bar Graphs
- used to compare amounts of the same type of measurement
Number of miles
Type of Car

7. -used to represent percentage data
Monthly Budget
Pie Graph
-used to represent percentage data

8. Line Graphs
-used for representing data that constantly changes at regular intervals
- may not necessarily show a regular pattern

9. 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

10. 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.

11. 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.

12. 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.

13. 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

14. Analyzing a Graph
Relationship 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)

15. Line Graphs – Kinds of Relationships
Classroom Exercise 1:
Line Graphs – Kinds of Relationships

16. Relationship – steady increase over a period of time
Curve is a straight line ~ since both factors are increasing the relationship is directly proportional

17. Relationship – increases over period of time until a max is reached and then decreases

18. Relationship – change over period of time then remains constant

19. Relationship – no change

20. Relationship – decrease over a period of time

21. Relationship – unchanged, decrease, remains constant

22. Building a Graph Identify the variables
Determine the range of each variable
Determine the scale (fill at least 2/3 of paper)
Number and label each axis
Plot the data points
Draw the graph
Title the graph (provide a key if needed)

23. “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.

24. KEY

25. Best Fit Line
Choose two points that you think will form the line of best fit. 
Best fit line may not go through the “O” point

27. Classroom Exercise 2: Draw a graph for this data
Time
(min)
Temperature
(ºC) 1
0.5
1.0 2
1.5 11
2.0 23
2.5 36
3.0 46
3.5 53
4.0 60
4.5 72
5.0 78
6.0 88
7.0
100
8.0
Classroom Exercise 2: Draw a graph for this data

29. Classroom Exercise 3: Building a Bar Graph
Month
Precipitation in Inches
January
0.78
February
0.96
March
2.03
April
3.10
May
4.29
June
4.02
July
3.85
August
3.26
September
2.91
October
2.31
November
1.76
December
1.10
Classroom Exercise 3: Building a Bar Graph

31. 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

33. Classroom Exercise 5: Interpolation and Extrapolation of Data

34. Classroom Exercise 6: Interpreting a Graph