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Homework
• Line of best fit page 1 and 2
Displaying and Describing
Categorical & Quantitative Data
You should be able to:
• Recognize when a variable is categorical or
quantitative
• Choose an appropriate display for a categorical
variable and a quantitative variable
• Summarize the distribution with stem-leaf plot,
histogram, dot plot, box plots
• Be able to describe the distribution of quantitative
variables in terms of its shape, center, spread, and
outliers.
Types of Graphs
•
•
•
•
Histogram
Dot plot
Stem leaf plot
Boxplots
Variables Come in 2 Varieties
1. Categorical (or Qualitative)
2. Quantitative (or Numerical)
1.
2.
Discrete
Continuous
Introduction to Statistics-Variables
5
Categorical Data
• The objects being studied are grouped into
categories based on some qualitative trait.
• Example: eye color, type of car you drive,
gender, etc.
Categorical Data
(Single Variable)
Eye Color
BLUE
BROWN
GREEN
Frequency
(COUNTS)
20
50
5
Relative
Frequency
20/75 =
0.27=27%
50/75=
0.66=66%
5/75=
0.07=7%
Quantitative Variables
• Variables that are numerical. They
represent a measurable quantity.
– Discrete: values that are only be whole
numbers
– Continuous: values that can be in decimals.
• Example: person’s height, # of
hamburgers sold each day of the week,
speed of a car, pulse rate, etc
Discrete vs Continuous data
Determine which one is a discrete and
continuous data
http://www.shmoop.com/probability-statistics/discrete-continuous-data-exercises.html
Go to  kahoot.it
Dot Plot
• Summarizes quantitative data.
• Horizontal axis represents measurement
scale.
• Plot one dot for each data point.
Dot Plot
Fastest Ever Driving Speed
226 Stat 100 Students, Fall '98
100
Men
126
Women
70
80
90
100 110 120 130 140 150 160
Speed
Stem-and-Leaf Plot
• Summarizes quantitative data
• Each data point is broken down into a “stem”
and a “leaf.”
• First, “stems” are aligned in a column.
• Then, “leaves” are attached to the stems.
Period 2: 57 60 88 85 79 70 65 98 97 59 58 65
62 77 77 75 73 69 82 81
Stem
5
Key: 7 9 means 79
Leaf
7 8 9
6
0 2 5 5 9
7
0 3 5 7 7 9
8
9
1 2 5 8
7 8
Histogram
• Summarizes quantitative data
• Divide measurement up into equal-sized
categories (BIN WIDTH)
• Determine number (or percentage) of
measurements falling into each category.
• Draw a bar for each category so bars’
heights represent number (or percent) falling
into the categories.
• Label and title appropriately.
Histogram
Age of Spring 1998 Stat 250 Students
50
40
30
20
10
0
18
19
20
21
22
23
24
Age (in years)
n=92 students
25
26
27
Strengths and Weaknesses
of Graphs for Quantitative Data
• Histograms
– Uses intervals
– Good to judge the “shape” of a data
– Not good for small data sets
• Stem-Leaf Plots
– Good for sorting data (find the median)
– Not good for large data sets
Strengths and Weaknesses
of Graphs for Quantitative Data
• Dotplots
– Uses individual data points
– Good to show general descriptions of
center and variation
– Not good for judging shape for large data sets
Finding Individuals & Variables
in a List
State
Region
Population
Males
Females
Alabama
Alaska
South
West
15.6m
5.4m
8.3m
2.5m
7.2m
2.9m
Arizona
West
10.2m
5.1m
5.1m
Individuals in Sample—Usually in 1st Column
Variables—Usually in 2nd and succeeding columns
Number of in Sample = 3
Who’s in Sample?
Alabama, Alaska, Arizona
Variable = Region
= Categorical
Variable = Population = Discrete Quantitative
Variable = Males =
Discrete Quantitative
Variable = Females = Discrete Quantitative
Look for Variable Names in Column Headings
Introduction to Statistics-Variables
18
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?
1)
2)
3)
4)
5)
6)
Length of a pen?
Type of pen?
Number of pens in box?
Maker of pen?
Flow of ink in ml/sec?
Color of pen’s ink?
Quantitative, Continuous
Categorical
Quantitative, Discrete
Categorical
Quantitative, Continuous
Categorical
Introduction to Statistics-Variables
19
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?

Subject of a book?

Number of pages in the book? Quantitative, Discrete

Area of each page of book?

Number of letters on a page?

Number of weeks on best
seller list?
Categorical
Quantitative, Continuous
Quantitative, Discrete
Quantitative, Discrete
Introduction to Statistics-Variables
20
Categorical or Quantitative
If Categorical, one possible category?
If Quantitative, Continuous or Discrete?
1)
2)
3)
4)
5)
6)
7)
Style of pants?
Color of pants?
Number of pairs of pants you own?
# of pockets on pants?
Size of pants?
Maker of the pants?
Length of inseam on the pants?
Introduction to Statistics-Variables
Categorical
Categorical
Quantitative, Discrete
__________________
categorical
Categorical
Quantitative,
Continuous
21