Chapter 2: Organizing and Summarizing Data
Section 2.1: Organizing Qualitative Data
Objectives: Students will be able to:
Organize qualitative data in tables
Construct bar graphs
Construct pie charts
Vocabulary:
Frequency Distribution – lists each category of data and the number of occurrences for each category of data
Relative Frequency Distribution – is the proportion (or percentage) of observations within a category
Bar Graph – a graph showing frequency or relative frequency on the y-axis and categories on the x-axis
Pareto chart – bar graph whose bars are drawn in decreasing order of frequency or relative frequency
Side-by-Side bar graphs – use relative frequency since sample or population sizes may be different
Pie Charts – circle divided into sectors; each sector represents a category of data; area is proportional to the frequency
of the category; all data must be represented
Key Concepts: Charts help to display data more visually with fewer words
Different Views
14
Rehab
Groin Neck
Hand 3% 3%
7%
12
10
Back
40%
Knee
17%
8
6
Rehab
4
Shoulder
13%
Hip
7%
Wrist
7%
Neck
Groin
Elbow
Hip
Hand
Shoulder
Rehab
Back
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Knee
Neck
Groin
Hand
Knee
Hip
Shoulder
Elbow
Wrist
Percent
Rehab
Elbow
3%
Wrist
Neck
Hand
Groin
Knee
Shoulder
Hip
Wrist
Elbow
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Back
Percent
0
Back
2
Plot in the lower right corner is a Pareto chart. It is the same as the relative frequency chart; except the categories are in
relative frequency order (from largest to smallest) from left to right. This graph came from the Total Quality Management
(TQM) era in the middle to late 1980’s.
Chapter 2: Organizing and Summarizing Data
Example:
Construct a frequency distribution and a histogram.
Below are the net weights (in ounces) of 30 cans of peas from the Grumpy Blue Midget Company.
16.2
15.7
16.4
15.4
16.4
15.8
16.0
15.2
15.7
16.6
15.8
16.2
15.9
15.9
15.6
15.8
16.1
15.9
16.0
15.6
16.3
16.8
15.9
16.3
16.9
15.6
16.0
16.8
16.0
16.3
Homework: pg : 67 – 73; 6-8, 11, 13, 15, 22, 30
Chapter 2: Organizing and Summarizing Data
Section 2.2: Organizing Quantitative Data: The popular displays
Objectives: Students will be able to:
Organize discrete data in tables
Construct histograms of discrete data
Organize continuous data in tables
Construct histograms of continuous data
Draw stem-and-leaf plots
Draw dot plots
Identify the shape of the distribution
Vocabulary:
Histogram – bar graphs of the frequency or relative frequency of the class
Classes – categories of data
Lower class limit – smallest value in the class
Upper class limit – largest value in the class
Class width – largest value minus smallest value of the class
Open Ended – one of the limits is missing (or infinite)
Stem-and-Leaf Plot – numerical graph of the data organized by place of the digits
Split stems – divides the digit (range) in half
Dot plots – like a histogram, but with dots representing the bars
Data distribution – determining from the histogram the shape of the data
Key Concepts:
Stem and Leaf plots maintain the raw data, while histograms do not maintain the raw data
Best used when the data sets are small
The number of classes, k, to be constructed can be roughly approximated by
k = number of observations
maximum - minimum
k
and always round up to the same decimal units as the original data.
To determine the width of a class use w =
Frequency Distributions
Uniform
Skewed (Right -- tail)
Normal (Bell-Shaped)
Skewed (Left -- tail)
Chapter 2: Organizing and Summarizing Data
With the following data
a) Construct a histogram
b) Construct a stem graph
Ex. 1
The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below.
22
20
Ex. 2
31
37
21
32
49
36
26
35
42
33
42
45
30
47
28
49
31
38
39
28
39
48
Below are times obtained from a mail-order company's shipping records concerning time from receipt of order to
delivery (in days) for items from their catalogue?
3
5
27
7
7
31
10
12
13
5
10
21
14
22
6
Homework: pg 87 - 96: 3, 6, 8, 9, 12, 14, 19, 28, 43
12
23
8
6
14
3
2
8
10
9
5
19
22
4
12
25
7
11
11
13
8
Chapter 2: Organizing and Summarizing Data
Section 2.3: Additional Displays of Quantitative Data
Objectives: Students will be able to:
Construct frequency polygons
Create cumulative frequency and relative frequency tables
Construct frequency and relative frequency ogives
Draw time-series graphs
Vocabulary:
Class midpoint – adding consecutive lower class limits and dividing by 2
Frequency polygon – Plot a point above each class midpoint on a horizontal axis at a height equal to the frequency of
the class. After points are plotted, straight lines (line-plot) are drawn between consecutive points
Cumulative Frequency Distribution – displays the aggregate frequency of the category
Cumulative Relative Frequency Distribution – displays the proportion (or percentage) of observations less than or equal
to the category for discrete data and less then or equal to the upper class limit for continuous data
Ogive – a line-plot graph that represents the cumulative frequency or cumulative relative frequency for the class
Time-Series Plot – plots (line-plots) time along the horizontal access and the corresponding variable value along the
vertical axis
Key Concepts:
Very similar to histograms
Comparative Stem and Leaf plots (back to back)
1.
Here are the numbers of home runs that Babe Ruth hit in his 15 years with the New York Yankees, 1920 to 1934.
54
49
59
46
35
41
41
34
46
22
25
47
60
54
46
Babe Ruth's home run record for a single year was broken by another Yankee, Roger Maris, who hit 61 home runs
in 1961. Here are Maris's home run totals for his 10 years in the American league.
13
23
26
16
33
61
28
39
14
8
Compare these two distributions by constructing a back-to-back stemplot. Comment on the similarities and/or
differences.
Homework: pg 101 - 104: 8, 11, 19
Chapter 2: Organizing and Summarizing Data
Section 2.4: Graphical Misrepresentations of Data
Objectives: Students will be able to:
Describe what can make a graph misleading or deceptive
Vocabulary:
None new
Key Concepts:
Common problems:
1. Vertical Axis
a. Inconsistent vertical scaling
b. Incorrect vertical scaling
c. Vertical axis that doesn’t start at zero
2. Scaling in pictures different than that reflected by the data
3. Class widths
a. Values overlap
b. Class widths different
Characteristics of Good Graphics:
1. Label the graphic clearly and provide explanations if needed
2. Avoid distortion. Don’t lie about the data
3. Avoid three-dimensions. Look nice, but often distract reader and result in misinterpretation
4. Don’t use more than one design in the same graphic.
a. Let the numbers speak for themselves
b. Sometimes graphs use a different design in a portion of the graphic to call attention to it
Example Data
2.23
2.22
2.21
2.2
2.18
Data
Comparing Two Graphs
Value
2.19
2.17
2.16
2.15
2.14
2.13
2.12
1
2
3
4
5
6
7
8
Category
Propaganda Chart
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
Value
1.5
1.4
1.3
1.2
1.1
Data
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
Category
Homework: pg 107-109: 1, 2, 7, 8, 13, 14
6
7
8
Chapter 2: Organizing and Summarizing Data
Chapter 2: Review
Objectives: Students will be able to:
Summarize the chapter
Define the vocabulary used
Complete all objectives
Successfully answer any of the review exercises
Use the technology to display graphs and plots of data
Vocabulary: None new
Homework: pg 111-117: 3, 5, 9, 11, 15, 19-21