Transcript Section 1.1 First Day Types of Variables, Pie Graphs, Bar Graphs

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Chapter 1: Exploring Data
Introduction – Data Analysis: Making Sense of Data
Section 1.1 – Analyzing Categorical Data
The Practice of Statistics, 4th edition - For AP*
STARNES, YATES, MOORE
 Data
Analysis is the process of organizing,
displaying, summarizing, and asking questions
about data.
Definitions:
Individuals – objects (people, animals, things)
described by a set of data
Variable - any characteristic of an individual
Categorical Variable
– places an individual into
one of several groups or
categories.
Quantitative Variable
– takes numerical values for
which it makes sense to find
an average.
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is the science of data.
Data Analysis
 Statistics
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Why the distinction is important
 You
will receive NO credit (really!) on the AP exam if
you construct a graph that isn’t appropriate for that
type of data
Type of Variable
Appropriate
Graph
Categorical
Pie Chart, Bar
Graph
Quantitative
Dotplot, Stemplot,
Histogram
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What type of variable?
 Yesterday,
I collected two data sets from you.
I asked you the fastest speed you’ve ever
driven and your favorite subject.
– quantitative or categorical?
 Subject – quantitative or categorical?
 Speed
Definition:
Distribution – tells us what values a variable
takes and how often it takes those values
Example
2009 Fuel Economy Guide
MODEL
2009 Fuel Economy Guide
2009 Fuel Economy Guide
MPG
MPG
MODEL
<new>MODEL
MPG
1
Acura RL
922 Dodge Avenger
1630 Mercedes-Benz E350
24
2
Audi A6 Quattro
1023 Hyundai Elantra
1733 Mercury Milan
29
3
Bentley Arnage
1114 Jaguar XF
1825 Mitsubishi Galant
27
4
BMW 5281
1228 Kia Optima
1932 Nissan Maxima
26
5
Buick Lacrosse
1328 Lexus GS 350
2026 Rolls Royce Phantom
18
6
Cadillac CTS
1425 Lincolon MKZ
2128 Saturn Aura
33
7
Chevrolet Malibu
1533 Mazda 6
2229 Toyota Camry
31
8
Chrysler Sebring
1630 Mercedes-Benz E350
2324 Volkswagen Passat
29
9
Dodge Avenger
1730 Mercury Milan
2429 Volvo S80
Variable of Interest:
MPG
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<new>
Dotplot of MPG
Distribution
Data Analysis
generally takes on many different values.
In data analysis, we are interested in how often a
variable takes on each value.
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 A variable
Population
Sample
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Data Analysis
From Data Analysis to Inference
Collect data from a
representative Sample...
Make an Inference
about the Population.
Perform Data
Analysis, keeping
probability in mind…
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The values of a categorical variable are labels for the
different categories
The distribution of a categorical variable lists the count or
percent of individuals who fall into each category.
Example, page 8
Frequency Table
Format
Variable
Values
Relative Frequency Table
Count of Stations
Format
Percent of Stations
Adult Contemporary
1556
Adult Contemporary
Adult Standards
1196
Adult Standards
8.6
Contemporary Hit
4.1
Contemporary Hit
569
11.2
Country
2066
Country
14.9
News/Talk
2179
News/Talk
15.7
Oldies
1060
Oldies
Religious
2014
Religious
Rock
869
Spanish Language
750
Other Formats
Total
1579
13838
7.7
14.6
Rock
6.3
Count
Spanish Language
5.4
Other Formats
11.4
Total
99.9
Percent
Analyzing Categorical Data
Variables place individuals into one of
several groups or categories
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 Categorical
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categorical data
Frequency tables can be difficult to read. Sometimes
is is easier to analyze a distribution by displaying it
with a bar graph or pie chart.
Frequency Table
Format
Relative Frequency Table
Count of Stations
Format
Percent of Stations
Adult Contemporary
1556
Adult Contemporary
Adult Standards
1196
Adult Standards
8.6
Contemporary Hit
4.1
Contemporary Hit
569
11.2
Country
2066
Country
14.9
News/Talk
2179
News/Talk
15.7
Oldies
1060
Oldies
Religious
2014
Religious
7.7
14.6
Rock
869
Rock
6.3
Spanish Language
750
Spanish Language
5.4
Other Formats
Total
1579
13838
Other Formats
11.4
Total
99.9
Analyzing Categorical Data
 Displaying
Good and Bad
Our eyes react to the area of the bars as well as
height. Be sure to make your bars equally wide.
Avoid the temptation to replace the bars with pictures
for greater appeal…this can be misleading!
This ad for DIRECTV
has multiple problems.
How many can you
point out?
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
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 Graphs:
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Introduction
Data Analysis: Making Sense of Data
Summary
In this section, we learned that…
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A dataset contains information on individuals.
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For each individual, data give values for one or more variables.
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Variables can be categorical or quantitative.
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The distribution of a variable describes what values it takes and
how often it takes them.
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Inference is the process of making a conclusion about a population
based on a sample set of data.
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Identify good and bad graphs – and label correctly!