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Type of variables:

Quantitative and Categorical

Types of Quantitative Variables

Discrete:

Listable values with gaps

between them.

Note: Not necessarily integers.

May be an infinite number of values.

Continuous:

Any value in an interval

can occur.

Categorical variable

A variable that classifies

people or things is

qualitativeor categorical.

Ex: gender, political affiliation,

race, country of origin.

Types of Categorical Variables

Nominal:

Values are simply labels or

categories.

Ex: 1 for Educator

2 for Construction worker

3 for Manufacturing worker

Types of Categorical Variables

Ordinal:

The categories have a naturalordering.

EX.

1 for President

2 for Vice President

3 for Dean of College

4 for Department Supervisor

5 for Employee

Types of Categorical Variables

Binary:Only two categories

(often labeled 0 and 1).

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Identify the type:

Height: Quantitative Continuous

Family Size: Quantitative Discrete

Age: Quantitative Continuous

Course Grade: CategoricalQualitative

Ordinal

Football jersey

number:

CategoricalQualitative

Nominal

Descriptive Inferential

NumericalGraphical

Statistics

Descriptive Statistics:

numerical summaries and/orgraphical displays of (sample) data.

Inferential Statistics:

Using sample data to makeconclusions about the population

from which the sample was taken.

Drawing conclusions about

the population (parameter),

based on a sample (statistic).

Statistical Inference

Population

Census

Real

Parameter

Sample

Statistic

estimates

After we collect data, then what?

Organize / Summarize Data

Graphical Numerical

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Graphs

Histogram

Stem-and-leaf plot

for a single

quantitative

variable

Bar Chart

Pie Chart

for a single

categorical

variable

Common Statistical Graphs Quantitative Data

Histogram- vertical bar chart of frequencies

- Frequency Polygon - line graph of frequencies

- Ogive - line graph of cumulative frequencies

Stem and Leaf Plot - Like a histogram, but shows

individual data values. Useful for small data sets.

Histogram

0

10

20

0 10 20 30 40 50 60 70 80

Years

Frequency

0

10

20

0 10 20 30 40 50 60 70 80

Years

Frequency

What values of Yearsfall in the 2nd class?

30 to 40

How many valuesfall in the 2nd class?

18 of the 50

What is the sum of theheights of all bars?

50

Frequency Polygon

- line graph of frequencies

Class Interval Frequency

20-under 30 6

30-under 40 18

40-under 50 11

50-under 60 11

60-under 70 3

70-under 80 10

10

20

0 10 2 0 3 0 4 0 50 6 0 7 0 8 0

Frequency

Years

Ogive

- line graph of cumulative frequencies

Cumulative

Class Interval Frequency

20-under 30 6

30-under 40 24

40-under 50 35

50-under 60 46

60-under 70 49

70-under 80 50 0

20

40

60

0 10 20 30 40 50 60 70 80

Years

Frequency

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Relative Frequency Ogive

Cumulative

Relative

Class Interval Frequency20-under 30 .12

30-under 40 .48

40-under 50 .70

50-under 60 .92

60-under 70 .98

70-under 80 1.000.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

0 10 20 30 40 50 60 70 80

Years

CumulativeRelativeFrequ

ency

Stem-and-leaf plot of Income1 N = 100

Leaf Unit = 1000

2 1 58

6 2 022330 2 555566667777778889999999

(22) 3 0001111222222222333344

48 3 5555555666777788889

29 4 00000001111223444

12 4 56667889

4 5 0

3 5 57

1 6

1 6

1 7 2

Stem-and-Leaf Plot

Stem-and-Leaf Plot

Purpose: Same as for a histogram, but provides a little more

detail about the data distribution.

Data values are split into stem and leaf components:

Choice of split is data dependent.

123 4 5.67

stem leaf discard

12,345.67

Distribution of a

Quantitative Variable

q Illustrated by a histogram ora stem-and-leaf plot.

q Indicates how the valuesof the variable are spread out

across the range of the variable.

Key Features of Data Distributions

Shape

Typical Value

Spread

Outliers

Shapes: Symmetric

Skewed right

Skewed left

Bimodal

(multi-modal)

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Frequency

Symmetric Distribution

Frequency

More or lessSymmetric Distribution

Frequency

Skewed Right

Frequency

Skewed Left

Frequency

Bimodal

Graphs

Histogram

Stem-and-leaf plot

for a single

quantitative

variable

Bar Chart

Pie Chart

for a single

categorical

variable

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This is NOTa histogram!

Bar Chart Common Statistical GraphsQualitative Data

Pie Chart -- proportional representation for

categories of a whole

Bar Chart frequency or relative frequency of

one more categorical variables

Second Quarter U.S. Truck Production

Second Quarter Truck

Production in the U.S.

(Hypothetical values)

2d QuarterTruck

ProductionCompany

A

B

C

D

ETotals

357,411

354,936

160,997

34,099

12,747920,190

Second Quarter U.S. Truck Production

Proportionofeach Truck production

Pie Chart Calculations for Company A

2d QuarterTruck

ProductionProportion DegreesCompany

A

B

C

D

E

Totals

357,411

354,936

160,997

34,099

12,747

920,190

.388

.386

.175

.037

.014

1.000

140

139

63

13

5

360

Pie Chart Calculations for Company A

2d QuarterTruck

ProductionProportion DegreesCompany

A

B

C

D

E

Totals

357,411

354,936

160,997

34,099

12,747

920,190

.388

.386

.175

.037

.014

1.000

140

139

63

13

5

360

357,411

920,190 =

=360.388

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Pareto Chart A pareto chart is a bar chart, sorted from most frequent to least

frequent, overlaid with a cumulative line graph (like an ogive).

0

10

20

30

40

50

60

70

80

90

100

Poor

Wiring

Short in

Coil

Defective

Plug

Other

Frequency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Graphs

Scatterplotfortwo

quantitative

variables

Scatterplot of Debt versus Income