Warm UpWho talks more—men or women? According to the author of The Female Brain, women say nearly three times as many words per day as men. Skeptical researchers devised a study to test this claim. They used electronic devices to record the talking patterns of 396 university students from Texas, Arizona, and Mexico. The device was programmed to record 30 seconds of sound every 12.5 minutes without the carrier’s knowledge. What were the results? According to a published report, “Men showed a slightly wider variability in words uttered….But in the end, the sexes came out just about even in the daily averages: women at 16,215 words and men at 15,669.”(a) Did researchers conduct an observational study or an experiment?

Explain.(b) Why was it important for the recording device to operate without the

knowledge of the carrier?(c) To what population can the results of this study be generalized?

Justify your answer.

Lesson 3: Organization of Data

Table 2.1 Level of Education of People 25 to 34 Years Old in the United States, 2007From Statistics Through Application pg. 37

Displaying Distributions within a Table

Classes:

Counts:

Rates:

Distribution:

Table 2.1 Level of Education of People 25 to 34 Years Old in the United States, 2007From Statistics Through Application pg. 37

ConsistencyRound off errors:

Table 2.1 Level of Education of People 25 to 34 Years Old in the United States, 2007From Statistics Through Application pg. 37

A bar graph (or bar chart) is a graphical display of data using bars of different heights.

Lets say you took a survey of your friends to find out which kind of movie they liked best. The results of the survey would look like this in a table.

Bar Graphs

Favorite Type of MovieComedy Action Romance Drama SciFi

4 5 6 1 4

Bar Graphs

Bar Graphs

Figure 2.1 Bar graph of the distribution of level of education for persons aged 25 to 34 in the United States in 2007.From Statistics Through Application pg. 38

Table 2.1 Level of Education of People 25 to 34 Years Old in the United States, 2007From Statistics Through Application pg. 37

Constructing a Bar Graph

STATE COSTIndiana 2.9¢

Oklahoma 4.3¢

Florida 6.0¢

Maine 3.8¢

Pennsylvania 5.8¢

Average cost per mile for passenger vehicles on state turnpikes

Step 1:Draw and label the x- and y-axes

Y-Axis

X-Axis

STATESFlorida

Pennsy.

OklahomaMaine

Indiana

6¢

5¢

4¢

3¢

2¢

1¢

CO

ST

Constructing a Bar Graph

Step 2:Draw the bars to the frequencies. Add a title.

Constructing a Bar Graph

STATESFlorida

Pennsy.

OklahomaMaine

Indiana

6¢

5¢

4¢

3¢

2¢

1¢

CO

STAverage cost per mile for passenger

vehicles on state turnpikes

Causes for Late Arrival Number of Occasions

Family Problems 8

Woke Up Late 20

Had to Take the Bus 4

Traffic tie-up 32

Sick 6

Bad Weather 3

Try one on your own:

Slept L

ate

REASONS

Traf

fic

Fam

ily

SickBu

s

30

25

20

15

10

5

FREQ

UEN

CY

35

Wea

ther

Different Reasons Why People Were Late to Work

Pareto ChartA type of bar graph displaying categorical variables, in which the frequencies are arranged in order from highest to lowest

Savings for the Softball TeamName Money Saved

Sue $53

Allen $75

Kirk $47

Steve $24

Grace $66

Constructing a Pareto Chart

Step 1:Rewrite and arrange the data from largest to smallest according to frequency.

Name Money SavedAllen $75Grace $66Sue $53Kirk $47Steve $24

Constructing a Pareto ChartStep 2: Construct and label the x- and y-axes.

$10

$60

$70

$50

$40

$30

$20

$80

Mon

ey S

aved

NameAllen

GraceSteveSue

Kirk

Y-Axis

X-Axis

Constructing a Pareto ChartStep 3:Draw the bars to the frequencies. Add title.

$10

$60

$70

$50

$40

$30

$20

$80

Mon

ey S

aved

Name

AllenGrace

SteveSueKirk

Savings for the Softball Team

Try One on Your OwnConstruct a Pareto Chart for the following data:

Kyle has a bag of marbles with 7 green, 8 brown, 4 purple, 6 orange, and 13 red.

Kyle’s Marbles

2

12

14

10864

Num

ber o

f Mar

bles

ColorsRed

Brown

PurpleGreen

Orange

Dot PlotsIn a Dot Plot, a set of data is represented by using dots over a number line. It is the simplest graph for displaying the distribution of a quantitative variable.

The frequency of the variables is represented by the dots.

Ages of Oscar Winners

Gender:Height:

M45

M59

M45

M42

M35

Gender:Height:

F39

F33

F25

F24

F32

Gender:Height:

M46

M28

M42

M36

M35

Gender:Height:

F32

F34

F27

F30

F30

Constructing a Dot PlotStep 1:Draw a horizontal line and mark it with a measurement scale (frequency range) that extends at least as low as the smallest value in the data set and as high as the largest value in the data set. Label the frequency range.

20 25 30 35 40 5045 55 60Ages

Constructing a Dot PlotStep 2:For each observation in the data set, locate the value on the measurement scale and represent it by a dot. If two or more observations have the same value, stack the dots vertically. Add title.

20 25 30 35 40 5045 55 60

Ages

Ages of Oscar Winners

Constructing Parallel Dot PlotsIt may be helpful to compare the distributions of female- and male-member ages. An effective way of doing this is to construct parallel dot plots.

20 25 30 35 40 5045 55 60Female

20 25 30 35 40 5045 55 60Male

Here, parallel lines are drawn for each gender. The same scale is used for both lines, and the lines are labeled.

Parallel Dot PlotsIs there a difference in the ages of the Oscar winners who were male and female?Comment on the similarities and differences that can be observed in the dot plot.

20 25 30 35 40 5045 55 60Female

20 25 30 35 40 5045 55 60Male

Try One on Your Own- Create a Dot PlotTable 2.3 Highway Gas Mileages for Model Year 2009

Midsize Cars

Figure 2.4 Minitab dotplot of EPA highway gas mileage ratings for 24 model year 2009 midsize cars.

Answer

Key ConceptThe purpose of a graph is to help us understand the data.

Ask, “What do I see?”

Key ConceptLook for patterns and deviations.

Key ConceptAn outlier in any graph of data is an individual observation that falls outside the overall pattern of the graph. An outlier is clearly separated from the main body of observations.

Many outliers are due to mistakes.

Key ConceptDoes it surprise you that the Bentley and Rolls-Royce midsize cars have much lower gas mileages than the other models?

BentleyArnage Rolls-Royce

Phantom

HomeworkChapter 1: (Monday’s lesson)

• Read pgs. 18-26 • On page 22 problems: 1.25, 1.26, 1.29• On page 26 problems:1.31, 1.32, 1.33

Chapter 2:• On pages 40 and 46 problems: 1.25,

1.26, 1.29, 1.31, 1.32, 1.33, 2.1, 2.2, 2.3, 2.4(b-c), 2.5(b), 2.7, 2.9, 2.10