Lesson 2.1Graphing Data

You will learn to…* display data in a circle graph and

a Pareto Graph* organize data in a stem-and-leaf plot and a dot plot* display data in a time series graph

Circle Graphs and

Bar Graphs are used to display

qualitative data.

A circle graph shows relationships of parts

to a whole.

It is easy to compare the size of each part to the whole.

Convert the frequency of each class into a percent.

Percents are used to label circle graphs.

Percent =

f n

then multiply by 100

Convert the frequency of each class into a degree.

Degrees are used to create circle graphs.

angle = percent · 360˚

n = 60

Cellular Phones

Type fRel

Freq. % Angle

T-Mobile 3

Sprint 1

Cingular 6

Nextel 30

Verizon 20

18˚

6˚

36˚

180˚120˚

360˚

.05

.02

.10

.50

.33

100%

5%

2%

10%50%33%

Cellular Phones

Sprint2%

T-Mobile5%

Cingular10%

Verizon33%

Nextel50%

A Bar Graph displaying qualitative data should be drawn

with space between bars of equal width.

It is easy to compare the sizes of the parts to each other.

n = 60

Cellular Phones

Type fRel

Freq. % Angle

T-Mobile 3

Sprint 1

Cingular 6

Nextel 30

Verizon 20

18˚

6˚

36˚

180˚120˚

360˚

.05

.02

.10

.50

.33

100%

5%

2%

10%50%33%

Cellular Phones

Nextel

353025201510 5N

umbe

r of

Pho

nes

Type of Service

Verizon

Cingular

T-Mobile

Sprint

n = 60

Cellular Phones

Type fRel

Freq. % Angle

T-Mobile 3

Sprint 1

Cingular 6

Nextel 30

Verizon 20

18˚

6˚

36˚

180˚120˚

360˚

.05

.02

.10

.50

.33

100%

5%

2%

10%50%33%

Cellular Phones

Nextel

Type of Service

Verizon

Cingular

T-Mobile

Sprint

.70

.60

.50

.40

.30

.20

.10Rel

ativ

e F

requ

ency

A Pareto chart is a bar graph

Bars in a Pareto chart are always arranged in descending order

Cellular Phones

Nextel

353025201510 5N

umbe

r of

Pho

nes

Type of Service

Verizon

Cingular

T-Mobile

Sprint

Practice A# 2.1.A

We display quantitative data to identify a pattern of variability.

One of the simplest graphs used is the dot plot.

In a dot plot each data entry is plotted (using a point) above a

horizontal axis.

It is similar to a bar graph but the display still contains the

original data values

60 65 70 75 80 85 90 95 100

Construct a Dot Plot for the following test scores of 20 students.

60 70 90 65 70 70 80 90 85 80 85 85 85 90 70 65 95 85 95 100

Stem-and-leaf plots provide an easy way to sort data.

Each number is separated into a “stem”

Similar to a bar graph but the display still contains the original

data values

Stem-and-Leaf Plot Key

Key: 4 | 5 = 45

Key: 11 | 6 = 116

Key: 12 | 3 = 12.3Data entries with 1 digit after the decimal

Two digit data entries

Three digit data entries

Always use consecutive integers for stems.

If there is no data for a stem, the leaf part is empty.

50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 88 41 78 56 72 56 17 7

Number of Minutes on the InternetStem-and-Leaf Plot

What stems should we use?

0123456 7 8

Key: 1| 6 = 16

Number of Minutes on the Internet

50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 88 41 78 56 72 56 17 7

Number of Minutes on the Internet

0 7 7 1 7 1 9 72 2 8 1 33 7 4 0 1 4 2 15 0 1 4 6 6 67 8 2 8 8

Key: 1| 6 = 16

Now, order the data

Number of Minutes on the Internet

0 7 7 1 7 1 9 72 2 8 1 33 7 4 0 1 4 2 15 0 1 4 6 6 67 8 2 8 8

Key: 1| 6 = 16Number of Minutes on the Internet

Does the Plot look like a bar graph?

Construct a stem-and-leaf plot and a dot plot for the following data set.

80 52 90 52 53 55 70 82 91 55 55 71 82 74 91 82 74 5575 85 93 85 93 76 56 76 93

5 2 2 3 4 5 5 5 5 667 0 1 4 4 5 6 6 8 0 2 2 2 5 5 9 0 1 1 3 3 3

Key: 6|4 is 64

50 55 60 65 70 75 80 85 90 95

Practice A# 2.1.B

A time series graph is a line graph used to show a pattern that occurs over a

period of time

Horizontal axis: year/monthVertical axis: number or percent

time series graph

> gas prices each week for 3 months

> # students enrolled at RV

> winning times in an Olympic race for the last 10 Olympics

> sales each month of one year

Month J F M A M J J A S O N DAverage price for a gallon of gas

$1.85$1.77$1.80$1.86$1.95$2.05$2.15$2.25$2.05$2.15$2.25$2.30

J F M A M J J A S O N D

2.402.302.202.102.001.901.801.701.60

Gas

Pric

e pe

r ga

llon

MONTH

Average Price Per Gallon of Gasoline

Practice A# 2.2.C