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