Example: Ages of wealthiest people
Notes
Frequency distribution table:
Ages of 50 Wealthiest People (2009)
Class Class Boundaries
35 - 41
34.5 - 41.5
42 - 48
41.5 - 48.5
49 - 55
48.5 - 55.5
56 - 62
55.5 - 62.5
63 - 69
62.5 - 69.5
70 - 76
69.5 - 76.5
77 - 83
76.5 - 83.5
84 - 90
83.5 - 90.5
2.1: Histogram
2.1: Relative Frequency Histogram
Frequency, f
2
5
7
7
10
5
8
6
Notes
Notes
2.1: Histograms
I
Create a column of class boundaries on the frequency distribution
table.
I
Start and end class boundaries by subtracting a value from the
lower limits (like 0.5 for whole numbers, 0.05 for data in tenths
place, etc...)
I
Draw a horizontal line for the data entries number line.
I
Draw a vertical line for the frequencies of the data.
I
Plot consecutive bars for each class and frequency.
Notes
For relative frequency histograms, scale the vertical line by relative
frequencies, not frequencies.
2.1: Ogive Example
2.1: Ogives
Graph a cumulative frequency.
I
Draw a horizontal scale of upper-class boundaries.
I
Draw a vertical scale measuring cumulative frequencies.
I
Plot points as a pair for each class:
(x, y ) = (upper-class boundary, cumulative frequency)
I
Connect the points in order with straight segments.
The graph should start at the lower boundary of the first class, where
the cumulative frequency is zero. It should end at the upper boundary
of the last class, where the cumulative frequency is the size of the
data set.
Notes
Notes
2.2: Stem-and-Leaf Example
Notes
Key: 3|5 = 35
3
4
5
6
7
8
|
|
|
|
|
|
56
234679
1133446789
0113455667899
23336788
01233566799
A stem is the entry’s left-most digits, a leaf is the right-most digit.
These are similar to histograms, but graph still contains all the data
values.
What is a disadvatage?
2.2: Dot Plot Example
Notes
Qualitative Data
Notes
Qualitative Data: Number of degrees conferred (in thousands) for
1990.
Type of Degree
Associate’s
Bachelor’s
Master’s
First Professional
Doctoral
Number (thousands)
455
1052
325
71
38
I
Use a pie chart, dividing a circle in sectors to represent categories.
I
Use a bar chart or Parteo chart, a vertical bar graph where the
height of bars are the frequencies.
2.2: Pie Chart Example
2.2: Pareto Chart (Bar Chart) Example
Assignment
For May 30:
I
Homework §2.1: #47, #48 (due June 2)
I
Homework §2.2: #36, #38, #39, #40 (due June 2)
Suggested Exercises: §2.1: 2, 3, 4, 5, 35; §2.2: 2, 9, 10, 11, 12, 17,
18
You should be able to:
I
Construct a histogram, relative frequency histogram, and ogive.
I
Construct a stem-and-leaf plot, box plot, and pie charts and
Pareto charts.
Notes
Notes
Notes