Twins Peter and Paul are twin brothers. One of them (we don’t know which) always lies. The other one always tells the truth. I ask one of them: “Is Paul.

Twins

Peter and Paul are twin brothers. One of them (we don’t know which) always lies. The other one always tells the truth. I ask one of them:

“Is Paul the one that lies?”

“Yes,” he answers.

Did I speak to Peter or Paul?

Twins

I spoke to Peter

Average Speed

On the way to his grandmother’s house, John travels at an average of 30 mph. On the way back, he travels at an average of 40 mph. What was his average speed for the entire trip?

Average Speed

Suppose the distance is 120 miles.

That means 4hrs there, 3hrs back.

That’s 240 miles / 7 hrs = 34.3 mph

Review of Last Couple of Weeks

Linear or Exponential?

a) Roach population grows 5% every 2 days.

b) Every year, 15 more students attend Matt Forte High School.

c) There has been a $100 increase in wage every 6 months.

Review of Last Couple of Weeks

x y

1 10

2 15

3 22.5

4 33.75

Linear or Exponential?

Review of Last Couple of Weeks

In how many years will a river expanding at 17.35% every year be three times its original size? Use Excel.

Making and Interpreting Graphs

Week 3

What do we use graphs for?

To better communicate information

Who uses graphs?

Newspapers Magazines Work meetings

What types of graphs are there?

Pie chart XY Graph Bar Chart

When do we use what?

Pie Chart Limited applicability Can be used only when you have a quantitative

variable associated with a list of categories where both the categories and the quantities each add up to a whole.

The categories must also be disjoint (no overlap) Common error: to use a pie chart on a set of

categories that do not make a whole and to use a pie chart when the categories overlap. 

Use percentage label when using a pie chart

Pie Chart Example[Source: Energy Information Administration]

Source Quadrillion BTU

Coal 22.87Petroleum 40.44Natural Gas 22.64Renewable Energy 5.98Nuclear 8.13Total 100.06

Pie Chart Example

Pie Chart Example

CoalPetroleumNatural GasRenewable EnergyNuclear

Pie Chart Example

Pie Chart Example

Pie Chart Example

Pie Chart Example

22.87; 23%

40.44; 40%

22.64; 23%

5.98; 6% 8.13; 8%

CoalPetroleumNatural GasRenewable EnergyNuclear

XY Graphs

AKA line graph (not necessarily a line) used when you have "a lot" of data points when categories along the x-axis are

numerical show trends in data clearly enable the viewer to make predictions

about the results of data not yet recorded

XY Graph ExampleLake Michigan/Lake Huron Water Levels (annual averages) 1988-2006

Year Level (meters)

1988 176.56421989 176.40081990 176.35001991 176.46921992 176.47921993 176.69581994 176.67831995 176.52751996 176.65421997 176.98421998 176.71671999 176.23582000 175.97672001 175.9508

2002 176.11832003 175.89172004 176.11082005 176.09002006 176.0158

XY Graph Example

Lake Michigan/Huron Water Level

175.8000

176.0000

176.2000

176.4000

176.6000

176.8000

177.0000

177.2000

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Year

Lev

el (

met

ers)

XY Graph Example

Lake Michigan/Huron Water Level y = -0.035x + 246.33

R2 = 0.394

175.8000

176.0000

176.2000

176.4000

176.6000

176.8000

177.0000

177.2000

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Year

Lev

el (

met

ers)

Bar Graph

use whenever there is a quantitative variable associated with the a categorical variable

For limited amount of data Succinct Easy to make comparisons within categories

and across categories Disadvantage: sometimes presents far too much

info. hard to make a single, clear point with them

Bar Graph ExamplePercentage of Home Heating Sources 1950, 1997

[Source: US Department of Energy]

Source 1950 1997

Coal 33.8% 0.2%Natural Gas 26.0% 51.2%Propane 2.3% 5.4%Fuel Oil 22.1% 10.2%Kerosene 3.0% 0.8%Electricity 0.6% 29.4%Wood 9.7% 1.8%No Heat Source 3.7% 0.6%Other 1.8% 0.4%

Bar Graph Example

Bar Graph Example

Coal

Natur

al G

as

Propa

ne

Fuel O

il

Keros

ene

Electri

city

Woo

d

No Hea

t Sou

rce

Oth

er0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

Series1Series2

Bar Graph Example

Bar Graph Example

Bar Graph Example

Coal

Natur

al G

as

Propa

ne

Fuel O

il

Keros

ene

Electri

city

Woo

d

No Hea

t Sou

rce

Oth

er0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

19501997

Guidelines for effective graph:

a.  What is the purpose of making a graph from this data?

b.  What type of graph should you make?          pie             bar          x-y scatter (line)   

c.  Decide on a title and consider the the W's (who, what, where and when)

d.  Legend:        yes      no e.  Descriptive x-axis label (if applicable) f.  Descriptive y-axis label (if applicable) g.  Scale (if applicable) h.   Source

Faulty Graphs

People can use graphs to tell you skewed, misleading information.

Faulty Graphs

Faulty Graphs

Faulty Graphs

Faulty Graphs

Faulty Graphs

Faulty Graphs

Example 1

Go to the qrc homepage. Under excel files, find IL_Pop_By_Race.xls and open it.

Add a column which contains the percentage of total population for each racial category.

Make an effective graph.

Guidelines for effective graph:

a.  What is the purpose of making a graph from this data?

b.  What type of graph should you make?          pie             bar          x-y scatter (line)   

c.  Decide on a title and consider the the W's (who, what, where and when)

d.  Legend:        yes      no e.  Descriptive x-axis label (if applicable) f.  Descriptive y-axis label (if applicable) g.  Scale (if applicable) h.   Source

Example 2

Go to the qrc homepage. Under excel files, find DePaulMajors04.xls and open it.

Make an effective graph.

Guidelines for effective graph:

a.  What is the purpose of making a graph from this data?

b.  What type of graph should you make?          pie             bar          x-y scatter (line)   

c.  Decide on a title and consider the the W's (who, what, where and when)

d.  Legend:        yes      no e.  Descriptive x-axis label (if applicable) f.  Descriptive y-axis label (if applicable) g.  Scale (if applicable) h.   Source

Make your own faulty graph

Change the scale of the y-axis.

Make your own faulty graph

Biolog

y

Englis

h

Inte

rnat

ional

Studie

s

Mat

hem

atics

Politic

al Scie

nce

0

100

200

300

400

500

20002004

Make your own faulty graph

Make your own faulty graph

Biolog

y

Englis

h

Inte

rnat

ional

Studie

s

Mat

hem

atics

Politic

al Scie

nce

200

250

300

350

400

450

500

20002004

Biolog

y

Englis

h

Inte

rnat

ional

Studie

s

Mat

hem

atics

Politic

al Scie

nce-100

100

300

500

700

900

1100

1300

1500

20002004

Example 3

Go to the qrc homepage. Under excel files, under the folder Chicago, find ChicagoPopulation1830-2000.xls and open it.

Make an effective graph.

Guidelines for effective graph:

a.  What is the purpose of making a graph from this data?

b.  What type of graph should you make?          pie             bar          x-y scatter (line)   

c.  Decide on a title and consider the the W's (who, what, where and when)

d.  Legend:        yes      no e.  Descriptive x-axis label (if applicable) f.  Descriptive y-axis label (if applicable) g.  Scale (if applicable) h.   Source

Example 4

What is wrong with this chart?

This week: Lab Activity 4 HW Assignment 3