1 Name _____________________________ Chapter 1 Learning Objectives Section Related Example on Page(s) Relevant Chapter Review Exercise(s) Can I do this? Identify the individuals and variables in a set of data. Intro 3 R1.1 Classify variables as categorical or quantitative. Intro 3 R1.1 Display categorical data with a bar graph. Decide whether it would be appropriate to make a pie chart. 1.1 9 R1.2, R1.3 Identify what makes some graphs of categorical data deceptive. 1.1 10 R1.3 Calculate and display the marginal distribution of a categorical variable from a two-way table. 1.1 13 R1.4 Calculate and display the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table. 1.1 15 R1.4 Describe the association between two categorical variables by comparing appropriate conditional distributions. 1.1 17 R1.5 Make and interpret dotplots and stemplots of quantitative data. 1.2 Dotplots: 25 Stemplots: 31 R1.6 Describe the overall pattern (shape, center, and spread) of a distribution and identify any major departures from the pattern (outliers). 1.2 Dotplots: 26 R1.6, R1.9 Identify the shape of a distribution from a graph as roughly symmetric or skewed. 1.2 28 R1.6, R1.7, R1.8, R1.9 Make and interpret histograms of quantitative data. 1.2 33 R1.7, R1.8 Compare distributions of quantitative data using dotplots, stemplots, or histograms. 1.2 30 R1.8, R1.10 Calculate measures of center (mean, median). 1.3 Mean: 49 Median: 52 R1.6 Calculate and interpret measures of spread (range, IQR, standard deviation). 1.3 IQR: 55 Std. dev: 60 R1.9 Choose the most appropriate measure of center and spread in a given setting. 1.3 65 R1.7 Identify outliers using the 1.5 × IQR rule. 1.3 56 R1.6, R1.7, R1.9 Make and interpret boxplots of quantitative data. 1.3 57 R1.7 Use appropriate graphs and numerical summaries to compare distributions of quantitative variables. 1.3 65 R1.8, R1.10
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1
Name _____________________________
Chapter 1 Learning Objectives Section
Related
Example
on Page(s)
Relevant
Chapter
Review
Exercise(s)
Can I do
this?
Identify the individuals and variables in a set of
data. Intro 3 R1.1
Classify variables as categorical or
quantitative. Intro 3 R1.1
Display categorical data with a bar graph.
Decide whether it would be appropriate to
make a pie chart.
1.1 9 R1.2, R1.3
Identify what makes some graphs of
categorical data deceptive. 1.1 10 R1.3
Calculate and display the marginal distribution
of a categorical variable from a two-way table. 1.1 13 R1.4
Calculate and display the conditional
distribution of a categorical variable for a
particular value of the other categorical
variable in a two-way table.
1.1 15 R1.4
Describe the association between two
categorical variables by comparing appropriate
conditional distributions.
1.1 17 R1.5
Make and interpret dotplots and stemplots of
quantitative data. 1.2
Dotplots: 25
Stemplots: 31 R1.6
Describe the overall pattern (shape, center, and
spread) of a distribution and identify any major
departures from the pattern (outliers).
1.2 Dotplots: 26 R1.6, R1.9
Identify the shape of a distribution from a
graph as roughly symmetric or skewed. 1.2 28
R1.6, R1.7,
R1.8, R1.9
Make and interpret histograms of quantitative
data. 1.2 33 R1.7, R1.8
Compare distributions of quantitative data
using dotplots, stemplots, or histograms. 1.2 30 R1.8, R1.10
Calculate measures of center (mean, median). 1.3
Mean: 49
Median: 52 R1.6
Calculate and interpret measures of spread
(range, IQR, standard deviation). 1.3
IQR: 55
Std. dev: 60 R1.9
Choose the most appropriate measure of center
and spread in a given setting. 1.3 65 R1.7
Identify outliers using the 1.5 × IQR rule. 1.3 56
R1.6, R1.7,
R1.9
Make and interpret boxplots of quantitative
data. 1.3 57 R1.7
Use appropriate graphs and numerical
summaries to compare distributions of
quantitative variables.
1.3 65 R1.8, R1.10
2
1.1 Analyzing Categorical Data
Read 2–4
Fr/Soph/Jr/Sr g.p.a
Email address
Name
Bus route
Phone number
Days absent
Address
Credits earned
Allergies
Current on immunizations
Exterior color mileage
Total car length
Number of cylinders
Cost
Model
VIN
Type of sound system
Size of fuel tank
What do we call these two kinds of variables? What’s the difference?
Why do people sometimes confuse the two kinds of variables?
What is a distribution? It’s all the values that a variable can take on and how often.
3
Alternate Example: Willott’s music
Here is information about 12 randomly selected songs in Willott’s music library.
…two-way table (2 variables are shown with counts or frequencies)
Senior Non-senior
Boy 8 3
Girl 15 4
…marginal distribution (totals for rows & columns; the distribution for each variable)
Senior Non-senior Totals
Boy 8 3 11
Girl 15 4 19
Totals 23 7 30
…conditional distribution (distribution of one variable as a % of the other variable)
Senior Non-senior
Boy 35% 43%
Girl 65% 57%
Totals 100% 100%
How do we know which variable to condition on? Divide by the explanatory variable totals.
Senior Non-senior Totals
Boy 73% 27% 100%
Girl 79% 21% 100%
Died Survived
Hospital A
Hospital B
5
What is a segmented (or stacked) bar graph?
Use a segmented bar graph to compare conditional distributions, to look for differences, and to look for
patterns.
When knowing the value of one variable helps predict the value of the other, we say that the variables are
associated. Association appears in a segmented bar graph when we see big differences in the proportions. The
proportions may be “flipped” or reversed.
Careful! An association does NOT
automatically mean that there is a
cause-and-effect relationship.
The boy/girl senior/non-senior graphs
did not show much association.
Alternate Example: Horseshoe Crabs
Two members of the University of Florida at Gainesville Department of Zoology collected data on Horseshoe
Crabs on a Delaware beach during 4 days in the late spring of 1992. Based on the color of the shells, they
classified each crab as Young, Intermediate, or Old and whether the crabs could right themselves when flipped
on their backs or whether they were stranded for at least a certain period of time. Here are the results.
Young Intermediate Old Total
Stranded 214 384 295 893
Not Stranded 1668 1204 216 3088
Total 1882 1588 511 3981
(a) Explain what it would mean if there was no association between age and strandedness.
(b) Does there appear to be an association between age and strandedness in this sample? Justify.
6
HW #12: page 22 (19, 21, 23, 25, 27–34)
And now, we change from categorical data to quantitative data…
1.2 Displaying Quantitative Data with Graphs Elmer and Ethel have retired and want to move someplace warm. The couple is considering nine different cities.
The dotplots below show the distribution of average daily high temperatures in December, January, and
February for each of these cities. Help them pick a city by answering the questions below, based on the data
shown in the graph.
1. What is the typical high temperature for these months in Phoenix, Orlando, and San Juan? Which of those 3 cities is
most similar in this respect to Palm Springs? (Look for the center: the average, median, or typical value.)
2. Are daily high temperatures for these months more predictable in Palm Springs or in Orlando? (Look at the spread:
the variation, including the range.)
3. What might be unique to Atlanta, San Diego, and Honolulu? (Look for outliers: unusual values.)
4. What makes San Juan and San Diego somewhat similar to one another? Likewise, Palm Springs, Phoenix, and
Orlando are similar to one another in this way, but different from the first group. (Look at the shape: symmetry vs.
asymmetry.)
palmspring...
atlantaH
phoenixH
sandiegoH
orlandoH
miamiH
keywestH
honoluluH
sanjuanH
60 65 70 75 80 85 90
Average High Temperatures Dot Plot
7
Read 25–27 Notice that we are now looking at quantitative data!
How should we describe the distribution of a quantitative variable? Use “SOCS”
Center- Typical value, such as the mean or the median
Spread- Range for now (we'll also use standard deviation and interquartile range "IQR")
Outliers- Unusual values for now (we'll eventually use the "1.5IQR Rule")
Shape- Address the graph's # of peaks and its symmetry