Let's zoom in on one corner of the coordinate plane. (This corner is called the first quadrant.) The point where the two

axes cross has a special name: it is called the origin.

The blue lines will help us find points. When you make your own graphs, you can use the lines on your graph paper to help you.

(0,0)

Finding Points in the Plane

We can find every point in the plane using two numbers. These numbers are called coordinates. We write a point's coordinates inside parentheses, separated by a comma, like this: (5, 6). Sometimes coordinates written this way are called an ordered pair.

The first number in an ordered pair is called the x-coordinate. The x-coordinate tells us how far the point is along the x-axis.

The second number is called the y-coordinate. The y-coordinate tells us how far the point is along the y-axis.

Estimating Points Sometimes, the point you

want to graph is in between points that are marked on the axes. When this happens, you must estimate where to put your point.

For example, graph

(5, 13) using these axes:

(5,13)

Some Rules for All Graphs

All of your graphs should have… A title

At the top of the graph and underlined It should represent what you are

graphing (use your variables)

Some Rules for All Graphs con’t Labeled Axis

Use a straight-edge to draw all lines Use the blue lines that are provided

for you on the graph paper. Axes should be drawn a few lines in

and up from the edge of the paper You must state what is represented

on the x-axis and what is represented on the y-axis; include units when necessary

Some Rules for All Graphs con’tThe appropriate scale

We need the graph to fill up the most paper. To find the right scale, we divide the range of the values by the number of tick marks on that axis. (Range is the highest value – the lowest value).

Then we round to a number that is easy to count by.

How to Graph Hold the graph paper

the tall way. Title it using the

variables. Label the axes; don’t

forget to include units. Draw axes a couple of

lines up and over Count the number of

lines going across the x-axis starting at the zero mark

20 lines

Distance vs. Time

Dis

tanc

e (m

)

Time (min)

Scale the x-axis Find your range for the x-axis

(in science it’s the highest data point because we always start from zero)

Time: 10-0=10 so range is 10 Divide the range of the x-axis

by the # of lines on the x-axis: 10/20=0.5

0.5 is an easy-to-count by number so count EVERY blue

line as 0.5

Time (min)

Distance (m)

0

1

2

3

4

5

6

7

8

9

10

Scale the x-axis:Distance vs. Time

Dis

tanc

e (m

)

Time (min)

0 1 2 3 4 5 6 7 8 9 10

Scale the y-axis

Repeat for the y-axis: tic marks = 30 lines

Range = 110/30=3.6667 so round to 5; Count the y-axis by 5s Could also count by 4s

Time (min)

Distance (m)

0 0

1 10

2 40

3 35

4 50

5 65

6 70

7 90

8 85

9 100

10 110

Nice Counting Numbers

Decimals:0.1

0.2

0.25

0.5

Whole Numbers:1251015202550100Etc.

Once in a while you might have to count by a different not so nice number!

Make Ordered Pairs (0,0) (1,10) (2,40) (3,35) (4,50) (5,65) (6,70) (7,90) (8,85) (9,100) (10,110)

0 1 2 3 4 5 6 7 8 9 10

1401301201101009080706050403020100

Time (min)

Dis

tanc

e (m

)

Distance vs. Time

Plot data

Relationship: The average distanced traveled is fairly constant for each time period.

Review:All Graphs need:

A title At the top and

underlined

Labeled Axes Axes scaled

appropriately (every tick mark increases by the same amount; each axes can be scaled differently)

Some Graphs need: A Key (when necessary) If you are

putting more than one line on a graph, it must have a key to distinguish the difference

Different Types of Graphs

Tables, charts and graphs are convenient ways to clearly show your data.

Circle (or Pie) Graph

There are three basic graph forms.

Notice on the next few slides how each of the following examples are used to illustrate the data.

Choose the best graph form to express your results.

Bar Graph Line Graph

Bar Graph A bar graph is used to show relationships

between groups. The two items being compared do not needto affect each other. It's a fast way to show big differences.Notice how easy it is to read a bar graph.

Chocolate Milk Sold

53

72

112

33

76

0

20

40

60

80

100

120

Monday Tuesday Wednesday Thursday Friday

Day

Amou

nt S

old

Monday TuesdayWednesday ThursdayFriday

Circle Graph or Pie Graph A circle graph is

used to show how a part of something relates to the whole.

This kind of graph is needed to show percentages effectively.

Chocolate Milk Sold

Monday

Tuesday

Wednesday

Thursday

Friday

Line Graph A line graph is

used to show continuing data; how one thing is affected by another.

It's clear to see how things are going by the rises and falls a line graph shows.

Chocolate MI lk Sold

0

20

40

60

80

100

120

Monday Tuesday Wednesday Thursday Friday

Day

Am

ount

Sol

d

Chocolate

Chocolate MI lk Sold

0

20

40

60

80

100

120

Monday Tuesday Wednesday Thursday Friday

Day

Am

ount

Sol

d

Chocolate

Chocolate Milk Sold

Monday

Tuesday

Wednesday

Thursday

Friday

Line Graph

Circle (Pie) Graph

The same data displayed in 3 different types of graphs.

Chocolate Milk Sold

53

72

112

33

76

0

20

40

60

80

100

120

Monday Tuesday Wednesday Thursday Friday

Day

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ount

Sol

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Monday TuesdayWednesday ThursdayFriday

Bar Graph

Choosing the Right Graph

Use a bar graph if you are not looking for trends (or patterns) over time; and the items (or categories) are not parts of a whole.

Use a pie chart if you need to compare different parts of a whole, there is no time involved and there are not too many items (or categories).

Use a line graph if you need to see how a Use a line graph if you need to see how a quantity has changed over time.  Line graphs quantity has changed over time.  Line graphs enable us to find trends (or patterns) over time.enable us to find trends (or patterns) over time.

More Examples of Different Graphs

Circle Graph

Used to show how the parts relate to the whole

Bar Graph

A bar graph contains horizontal or vertical bars.

A good way to compare data that can be grouped into a category.

The bars do not touch.

Memberships in after-school clubs

0

10

20

30

40

50

60

70

Compute

r

Studen

t Counci

l

Dram

a

Mat

h Counts

Clubs after school

Nu

mb

er

of

Stu

de

nts

Column 1

HistogramsHistograms

Special type of bar graph

Compares different intervals of data rather than categories

The ranges used for the intervals must be the same size

Bars should touch

Line Graphs

Drawn dot-to-dot Shows trends To compare trends

between two or more things, you plot different lines for each and include a key

Scatter Plot

A scatter plot is a graph made by plotting ordered pairs in a coordinate plane to show the correlation between two sets of data.

x-variable

y-va

riabl

e

How do you determine the best-fit line through data points?

x-variable

y-variableTry to get an even number of data points on the line and on each side of the ruler

Positive Correlation

A scatter plot describes a positive trend if, as one set of values increases, the other set tends to increase. 

Negative Correlation

A scatter plot describes a negative trend if, as one set of values increases, the other set tends to decrease.

No Trend

A scatter plot shows no trend if the ordered pairs show no correlation