Transcript Frequency Distributions A frequency distribution is a table used to organize data.

Frequency Distributions
A frequency distribution is a table used to organize
data. The left column (called classes or groups)
includes numerical intervals on a variable being
studied. The right column is a list of the
frequencies, or number of observations, for each
class. Intervals are normally of equal size, must
cover the range of the sample observations, and be
non-overlapping.
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Construction of a Frequency
Distribution
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Rule 1: Intervals (classes) must be inclusive and
non-overlapping;
Rule 2: Determine k, the number of classes;
Rule 3: Intervals should be the same width, w;
the width is determined by the following:
(Largest Number - Smallest Number)
w  Interval Width 
Number of Intervals
Both k and w should be rounded upward, possibly to the next
largest integer.
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Construction of a Frequency
Distribution
Quick Guide to Number of Classes for a Frequency
Distribution
Sample Size
Fewer than 50
50 to 100
over 100
Number of Classes
5 – 6 classes
6 – 8 classes
8 – 10 classes
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Cumulative Frequency
Distributions
A cumulative frequency distribution contains the
number of observations whose values are less
than the upper limit of each interval. It is
constructed by adding the frequencies of all
frequency distribution intervals up to and
including the present interval.
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Relative Cumulative Frequency
Distributions
A relative cumulative frequency
distribution converts all cumulative
frequencies to cumulative
percentages
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Histograms and Ogives
A histogram is a bar graph that consists of
vertical bars constructed on a horizontal line
that is marked off with intervals for the
variable being displayed. The intervals
correspond to those in a frequency
distribution table. The height of each bar is
proportional to the number of observations
in that interval.
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Histograms and Ogives
An ogive, sometimes called a cumulative
line graph, is a line that connects points
that are the cumulative percentage of
observations below the upper limit of each
class in a cumulative frequency
distribution.
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Histogram and Ogive for Example 2.1
Histogram of Weights for Example 2.1
40
100
90
35
80
70
Frequency
30
25
60
50
40
20
15
30
20
10
5
10
0
0
224.5
229.5
234.5
239.5
244.5
249.5
Interval Weights (mL)
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Stem-and-Leaf Display
A stem-and-leaf display is an exploratory data analysis
graph that is an alternative to the histogram. Data are
grouped according to their leading digits (called the
stem) while listing the final digits (called leaves)
separately for each member of a class. The leaves are
displayed individually in ascending order after each of
the stems.
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Stem-and-Leaf Display
Stem-and-Leaf Display for Gilotti’s Deli
Example
Stem-and-Leaf Display
Stem unit: 10
9
(9)
7
2
1
2
3
4
124678899
122246899
01234
02
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Tables
- Bar and Pie Charts Frequency and Relative Frequency Distribution for
Top Company Employers Example
Industry
Tourism
Retail
Health Care
Restaurants
Communications
Technology
Space
Other
Number of
Employees Percent
0.35
85,287
0.2
49,424
0.16
39,588
0.06
16,050
0.05
11,750
0.05
11,144
0.05
11,418
0.08
21,336
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Tables
- Bar and Pie Charts Figure 2.9 Bar Chart for Top Company
Employers Example
1999 Top Company Employers in Central Florida
0.35
0.2
0.16
0.05
0.08
O
th
er
Re
st
au
ra
Co
nt
s
m
m
un
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t io
ns
Te
ch
no
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0.05
Sp
ac
e
0.05
ar
e
C
He
al
th
Re
ta
il
To
ur
ism
0.06
Industry Category
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Tables
- Bar and Pie Charts Figure 2.10 Pie Chart for Top Company
Employers Example
1999 Top Company Employers in Central Florida
Others
29%
Health Care
16%
Tourism
35%
Retail
20%
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Pareto Diagrams
A Pareto diagram is a bar chart that displays the
frequency of defect causes. The bar at the left
indicates the most frequent cause and bars to the
right indicate causes in decreasing frequency. A
Pareto diagram is use to separate the “vital few”
from the “trivial many.”
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Line Charts
A line chart, also called a time plot, is a series of data
plotted at various time intervals. Measuring time along
the horizontal axis and the numerical quantity of interest
along the vertical axis yields a point on the graph for
each observation. Joining points adjacent in time by
straight lines produces a time plot.
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Line Charts
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Age 18 to 29
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Millions of Adults
Growth Trends in Internet Use by Age
1997 to 1999
Age 30 to 49
Age 50+
April 1997 to July 1999
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