Transcript Qualitative (Categorical) Data

1.1 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 a bar, pie chart, stemleaf 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
•
•
•
•
•
Bar graph
Histogram
Dot plot
Stem leaf plot
Boxplots
Which graph to use?
• Depends on type of data
– For categorigal you will typically
use either a bar or pie graph
– For quantitative you can use
dotplot, stemplot, histogram,
boxplot.
Categorical Data
• The objects being studied are grouped into
categories based on some qualitative trait.
• Can use either use frequency (count) or relative
frequency (percentages) to express data
ex- 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 =
.27
50/75=
.66
5/75=
.07
Pie Chart
(Data is Counts or Percentages)
Eye Color
Green, 5, 7%
Blue , 20, 27%
Brown, 50, 66%
Blue
Brown
Green
Bar Graph
(Shows distribution of data)
Eye Color
Frequency
60
50
40
Blue
30
20
10
0
Brown
Green
Blue
Brown
Color
Green
Quantitative Variables
• Variables that are numerical. They
represent a measurable quantity.
• Ex- person’s height, # of hamburgers sold each
day of the week, speed of a car, pulse rate, etc
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.
Here are the scores from two periods of math
class. Students took the same test.
Period 1: 77 79 85 58 97 94 82 81 75 63 60 92 75
98 83 58 72 57 70 81
Period 2: 57 60 88 85 79 70 65 98 97 59 58 65 62
77 77 75 73 69 82 81
Period 1: 76 79 85 58 97 94 82 81 75 63 60 92
75 98 83 58 72 57 70 81 Notice that the data (numerical facts)
A key
should be
included
when
making a
stemand-leaf
plot.
Stem
5
Leaf
8 8 7
are numbers between 57-98. Create the
stem by listing numbers from 5-9.
Stem
Leaf
6
3 0
5
7 7 8
7
6 9 5 5 2 0
6
0 3
7
0 2 5 5 6 9
8
1 1 2 3 5
9
2 4 7 8
8
5 2 1 3 1
9
7 4 2 8
Key: 7 9 means 79
Rearrange
the leaf in
numerical
order from
least to
greatest
Match up the data to the stem-and-leaf. The last digit in 76 will match up with the stem 7.
Then the last digit in 79 will match up with the stem 7. Then the last digit in 85 will match
up with the stem 8 and this pattern will continue until all data have been recorded in the
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
• 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
Use common sense in
determining number of
categories to use.
Between 5 & 15 intervals
is preferable
Too few categories
Age of Spring 1998 Stat 250 Students
60
50
40
30
20
10
0
18
23
Age (in years)
n=92 students
28
Too many categories
GPAs of Spring 1998 Stat 250 Students
7
Frequency (Count)
6
5
4
3
2
1
0
2
3
GPA
n=92 students
4
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
Summary
• Many possible types of graphs.
• Use common sense in reading graphs.
• When creating graphs, don’t summarize your
data too much or too little.
• When creating graphs, label everything for
others.
Remember you are trying to communicate
something to others!