1. 2.1 Organizing Qualitative Data
Creating Bar Charts and Pie Charts

2. Frequency Vs. Relative Frequency
A frequency distribution lists each category of data and the number of occurrences for each category of data.
The relative frequency is the proportion (or percent) of observations within a category and is found using the formula:
A relative frequency distribution lists the relative frequency of each category of data.

4. Bar Graphs
A bar graph is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis.
A Pareto chart is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency.
Use the M&M data to construct
a frequency bar graph and
a relative frequency bar graph.

5. Frequency Bar Graph

6. Relative Frequency Bar Graph

7. Pareto Chart of M&M’s

8. Comparing Two Data Sets
The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in 1990 and 2006.
Draw a side-by-side relative frequency bar graph of the data.
Marital Status
1990
2006
Never married
40.4
55.3
Married
112.6
127.7
Widowed
13.8
13.9
Divorced
15.1
22.8

9. Side-by-Side Bar Graph

10. Copyright © 2010 Pearson Education, Inc.
What percentage of college students get their information from television?
181%
32.9%
45.3%
60.3%
Copyright © 2010 Pearson Education, Inc.
Slide 2- 10 10

11. Pie Charts A pie chart is a circle divided into sectors.
Each sector represents a category of data.
The area of each sector is proportional to the frequency of the category.

12. Favorite Colors of 15 Friends
Using a Calculator
You can use a calculator to create graphs ONLY if you have raw data. You cannot use a frequency distribution in the calculator.
Favorite Colors of 15 Friends
Blue
Green
Red
Pink
Yellow
YES!
NO!

13. TI-nspire Qualitative Data
Create a new lists & spreadsheets
Title column
Enter data into column
Create a new Data & Statistics Page
Click on x-axis box to add variable – choose, the name you just created
Click Menu and change graph type to desired graph.
Create a dot plot, bar chart, and pie chart for the following data.
Favorite Colors of 15 Friends
Blue
Green
Red
Pink
Yellow

14. 2.2 Organizing Quantitative Data
The first step in summarizing quantitative data is to determine whether the data is discrete or continuous.
If the data is discrete and there are relatively few different values of the variable, the categories of data will be the observations (as in qualitative data).
If the data is discrete, but there are many different values of the variable, or if the data is continuous, the categories of data (called classes) must be created using intervals of numbers.

15. Constructing Frequency and Relative Frequency Distribution from Discrete Data
The following data represent the number of available cars in a household based on a random sample of 50 households.
Construct a frequency and relative frequency distribution.

17. Histograms
A histogram is constructed by drawing rectangles for each class of data whose height is the frequency or relative frequency of the class.
The width of each rectangle should be the same and they should touch each other.

18. Histograms
Draw a frequency and relative frequency histogram for the “number of cars per household” data.

19. Number of cars per household

20. Continuous Data
Categories of data are created for continuous data using intervals of numbers called classes.
The following data represents the number of persons aged who are currently work disabled.
The class width is the difference between consecutive lower class limits. The class width of the data given above is = 10.

21. Continuous Data
The lower class limit of a class is the smallest value within the class
The lower class limit of first class is 25.
The lower class limit of the second class is 35.
The upper class limit of a class is the largest value within the class.
The upper class limit of the first class is 34.

22. Guidelines Should be between 5 and 20 classes
Choose a class width the you think will summarize the data well
Try to avoid open ended classes
60 and older
Watch out for tables with class widths that overlap
Class of and 30-40

23. Sample Problem - Organizing Continuous Data into a
Sample Problem - Organizing Continuous Data into a Frequency and Relative Frequency Distribution
The following data represent the time between eruptions (in seconds) for a random sample of 45 eruptions at the Old Faithful Geyser in California. Construct a frequency and relative frequency distribution of the data.

24. The smallest data value? The largest data value?
Sample Problem - Organizing Continuous Data into a Frequency and Relative Frequency Distribution
The smallest data value?
672, so maybe we should start the class at 670?
The largest data value?
738, so maybe we should end the class at 740?

25. Now select a width…maybe 5 or 10? See what looks good with the data.
Sample Problem - Organizing Continuous Data into a Frequency and Relative Frequency Distribution
Now select a width…maybe 5 or 10? See what looks good with the data.
670 –
675 –
680 –
685 –
690 –
695 –
700 –

28. Using class width of 10:

29. Using class width of 5:

30. Copyright © 2010 Pearson Education, Inc.
Find the class width. 3 4 5 19
Class
Frequency, f
1 – 5 21
6 – 10 16
11 – 15 28
16 – 20 13
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Slide 2- 30 30

31. Copyright © 2010 Pearson Education, Inc.
Identify the type of graph shown.
Bar Graph
Pie Chart
Pareto Chart
Histogram
Copyright © 2010 Pearson Education, Inc.
Slide 2- 31 31

32. Copyright © 2010 Pearson Education, Inc.
Which class has the highest frequency? 53 58
18 – 22
18 – 23
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Slide 2- 32 32

33. Stem-and-Leaf Plot
A stem-and-leaf plot uses digits to the left of the rightmost digit to form the stem.
Each rightmost digit forms a leaf.
For example, a data value of 147 would have 14 as the stem and 7 as the leaf.
2 8
7 5
8 5

34. © 2010 Pearson Prentice Hall. All rights reserved
State
Unemployment Rate
Alabama
4.7
Kentucky
6.3
North Dakota
3.2
Alaska
6.8
Louisiana
3.8
Ohio
6.6
Arizona
4.8
Maine
5.3
Oklahoma
3.9
Arkansas
5.0
Maryland
4.0
Oregon
5.5
California
6.9
Mass
5.2
Penn
Colorado
5.1
Michigan
8.5
Rhode Island
7.5
Conn
5.4
Minnesota
South Carolina
6.2
Delaware
4.2
Mississippi
South Dakota
2.8
Dist Col
6.4
Missouri
5.7
Tenn
6.5
Florida
Montana
4.1
Texas
4.4
Georgia
Nebraska
3.3
Utah
Hawaii
Nevada
Vermont
Idaho
New Hamp
Virginia
Illinois
New Jersey
Washington
Indiana
5.8
New Mexico
W. Virginia
Iowa
New York
Wisconsin
4.6
Kansas
4.3
North Carolina
6.0
Wyoming
© 2010 Pearson Prentice Hall. All rights reserved 34

35. Sample Problem
An individual is considered to be unemployed if they do not have a job, but are actively seeking employment. The following data represent the unemployment rate in each of the fifty United States plus the District of Columbia in June, 2008.
We let the stem represent the integer portion of the number and the leaf will be the decimal portion.
For example, the stem of Alabama will be 4 and the leaf will be 7.
2 8
7 5
8 5
2 8
7 5
8 5

36. Stem-and-Leaf Plot

37. A split stem-and-leaf plot: Best used when data appears bunched up
2 8
7 5
8 5
This stem represents 3.0 – 3.4
This stem represents 3.5 – 3.9
2-37 37

38. Advantage of Stem-and-Leaf Diagrams over Histograms
Once a frequency distribution or histogram of continuous data is created, the raw data is lost (unless reported with the frequency distribution)
However, the raw data can be retrieved from the stem-and-leaf plot.
Stem-and-leaf plots are best used when the data set is SMALL

39. Copyright © 2010 Pearson Education, Inc.
What is the maximum data entry? 96 38 79 56
Key: 3 | 8 = 38
Copyright © 2010 Pearson Education, Inc.
Slide 2- 39 39

40. Dot Plot
A dot plot is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed.

41. Dot Plot
The following data represent the number of available cars in a household based on a random sample of 50 households.
Draw a dot plot of the data.
Data based on results reported by the United States Bureau of the Census.

42. Dot Plot

43. Distribution Shape

44. Copyright © 2010 Pearson Education, Inc.
True or false: The distribution is skewed right.
True
False
Copyright © 2010 Pearson Education, Inc.
Slide 2- 44 44

45. TI-nspire Quantitative Data
Create a new lists & spreadsheets
Title column
Enter data into column
Create a new Data & Statistics Page
Click on x-axis box to add variable – choose, the name you just created
Click Menu and change graph type to histogram
Create a Histogram for the following data
40 Randomly Selected yr. olds.
Serum HDL Cholesterol 70 54 28 36 66 53 45 38 58 44 56 46 63 51 48 55 33 35 49 52 73 60 62 32 39 69 50