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Mini-Lecture 2.1 Organizing Qualitative Data Objectives

1. Organize qualitative data in tables 2. Construct bar graphs 3. Construct pie charts

Examples

1. The 2000 Census results include a summary of the racial composition of the population. The races reported by the populations of the United States and the State of California are summarized below. The data are given in millions. (Source: census.gov)

Race U.S. California White 211.5 26.4 Black 34.7 2.4 Asian 10.2 3.8 American Indian 2.5 0.4 Pacific Islands 0.4 0.1 Other single race 15.4 0.5 Two or more races 6.8 0.8

a. Construct a relative frequency distribution for races in the U.S.

Relative Frequency

Race (U.S.) White 0.7513 Black 0.1233 Asian 0.0362 American Indian 0.0089 Pacific Islands 0.0014 Other single race 0.0547 Two or more races 0.0242

b. What percentage of U.S. residents claims two or more races? (2.42%) c. What percentage of U.S. residents is not white? (24.87%) d. Construct a frequency bar graph for races in the U.S.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

e. Construct a relative frequency bar graph for races in the U.S.


f. Construct a pie chart for races in the U.S.


2. Use the data in Problem 1 to answer this question.

a. Construct a relative frequency distribution for the races in California.

Relative Frequency Race (California) White 0.7674 Black 0.0698 Asian 0.1105 American Indian 0.0116 Pacific Islands 0.0029 Other single race 0.0145 Two or more races 0.0233


b. What percentage of California residents claims two or more races?

(2.33%) c. What percentage of California residents is not white? (23.26%) d. Construct a frequency bar graph for California.


e. Construct a relative frequency bar graph for California.


f. Construct a pie chart for California.

In-Class Activity

(Requires one bag of multicolored candy, such as M&M’s or Skittles for each student.) Ask the students bring one bag of candy, such as M&M’s or Skittles to class. Have them create a frequency distribution of the counts of each color of candy in their bag. Have the students create a bar graph, relative frequency bar graph, and a pie chart illustrating the number of each type they observed.


Mini-Lecture 2.2 Organizing Quantitative Data: The Popular Displays Objectives

1. Organize discrete data in tables 2. Construct histograms of discrete data 3. Organize continuous data in tables 4. Construct histograms of continuous data 5. Draw stem-and-leaf plots 6. Draw dot plots 7. Identify the shape of a distribution

Examples

1. Every six months, the United States Federal Reserve Board conducts a survey of credit card plans in the U.S. The following data are the interest rates charged by 10 credit card issuers randomly selected for the January 2008 survey. (Source: http://www.federalreserve.gov/pubs/SHOP/survey.htm)

Institution Rate Pulaski Bank and Trust Company 6.5%Rainier Pacific Savings Bank 12.0%Wells Fargo Bank NA 14.4%Firstbank of Colorado 14.4%Lafayette Ambassador Bank 14.3%Infibank 13.0%United Bank, Inc. 13.3%First National Bank of The Mid-Cities 13.9%Bank of Louisiana 9.9%Bar Harbor Bank and Trust Company 14.5%

With the first class having a lower class limit of 6% and a class width of 3%,

a. Construct a frequency distribution for the distribution of interest rates among the banks surveyed.

Class Frequency Relative Frequency 6-8.99 1 0.1 9-11.99 1 0.1

12-14.99 8 0.8

b. Construct a relative frequency distribution for the distribution of interest rates among the banks surveyed. (See above)

c. Construct a histogram of the data.


http://www.federalreserve.gov/pubs/SHOP/survey.htm

d. Construct a relative frequency histogram of the data.

e. Describe the shape of the distribution. (Left-skewed)


f. Repeat parts (a)-(e) using a class width of 1%.

Class Frequency Relative Frequency 6-6.99 1 0.1 7-7.99 0 0.0 8-8.99 0 0.0 9-9.99 1 0.1

10-10.99 0 0.0 11-11.99 0 0.0 12-12.99 1 0.1 13-13.99 3 0.3 14-14.99 4 0.4

(The distribution appears to be left skewed)


g. Which frequency distribution seems to provide a better summary of the data? (The shape of the distribution seems most apparent when a class width of 1% is used, although answers may vary.)


2. There are 435 representatives in the U. S. House of Representatives. The number for each state is based on the state population. Based on the 2000 census, the number of representatives for each state is summarized in the table below. (Source: census.gov/population/cen2000/tab01.pdf)

Count States 1 AK DE MT ND SD VT WY 2 HI ID ME NH RI 3 NE NM NV UT WV 4 AR KS MS 5 CT IA OK OR 6 KY SC 7 AL CO LA 8 AZ MD MN WI 9 IN MO TN WA

10 MA 11 VA 13 GA NC NJ 15 MI 18 OH 19 IL PA 25 FL 29 NY 32 TX 53 CA

With the first class having a lower class limit of 0 and a class width of 5,

a. Construct a frequency distribution for the number of states with a specified number of representatives.

Class Frequency Relative Frequency 0-4.99 20 0.40 5-9.99 17 0.34

10-14.99 5 0.10 15-19.99 4 0.08 20-24.99 0 0.00 25-29.99 2 0.04 30-34.99 1 0.02 35-39.99 0 0.00 40-44.99 0 0.00 45-49.99 0 0.00 50-54.99 1 0.02

b. Construct a relative frequency distribution for the number of states with a

specified number of representatives. (See above) c. Construct a histogram of the data.


d. Construct a relative frequency histogram of the data.

e. Describe the shape of the distribution. (Right-skewed) f. Repeat parts (a)-(e) using a class width of 10.

Class Frequency Relative Frequency 0-9.99 37 0.74

10-19.99 9 0.18 20-29.99 2 0.04 30-39.99 1 0.02 40-49.99 0 0.00 50-59.99 1 0.02


(The distribution appears to be right skewed)

g. Which frequency distribution seems to provide a better summary of the data? (Answers may vary, but the detail provided with the class width of 5 may be desirable in this case.)

h. Make a stem-and-leaf plot of this data. 0 11111112222233333444 0 55556677788889999 1 01333 1 5899 2 2 59 3 2 3 4 4 5 3

i. Draw a dot plot summarizing this data.


j. Which three states have the largest population? (In decreasing order:

California, Texas, New York) In-class Activities

1. Ask the students to compute their heights (in inches). Randomly select some students to report their heights. Create a histogram of the students’ heights. It would be good to make a histogram for men and a histogram for women. Ask the students to identify the shape of the distribution.

2. Make a histogram showing the number of full-blooded siblings each student has. (An only child will have zero siblings.)


Mini-Lecture 2.3 Additional Displays of Quantitative Data Objectives

1. Construct frequency polygons 2. Create cumulative frequency and relative frequency tables 3. Construct frequency and relative frequency ogives 4. Draw time-series graphs

Examples

1. A simple random sample of 4,000 women who gave birth in the year 2005 was collected. The following table summarizes the mother’s ages at the time they gave birth. (Based on data at: http://www.infoplease.com/ipa/A0005074.html)

Age of Mother 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 Frequency 9 401 1006 1094 919 467 101 6

a. Create a cumulative frequency table summarizing the data.

Age of Mother Frequency

Cumulative Frequency

Relative Frequency

Cumulative Relative

Frequency 10-14 6 6 0.0015 0.0015 15-19 401 407 0.1003 0.1018 20-24 1006 1413 0.2515 0.3533 25-29 1094 2507 0.2735 0.6268 30-34 919 3426 0.2298 0.8565 35-39 467 3893 0.1168 0.9733 40-44 101 3994 0.0253 0.9985 45-54 6 4000 0.0015 1.0000

b. Create a relative frequency table of the data. (See above) c. Create a cumulative relative frequency table for the data. (Note: answers

may vary slightly due to rounding.) d. Construct a frequency ogive for the data.


http://www.infoplease.com/ipa/A0005074.html

e. Construct a relative frequency ogive for this data.


2. The stock price of Google, Inc. at the end of each year from Sept. 2004 through Sept. 2005 is given below (Source: tradingcharts.com.)

Year 2004 2005 2006 2007 Price 192.79 414.86 460.48 691.48

Make a time-series graph showing the price of Google’s stock at the end of each of these years.

3. Does the growth of New York City appear to be constant over time, or does it

fluctuate dramatically? The data below represent the change in the population over each decade. Negative values imply a population decrease. (Source: census.gov.)

End of Decade 1960 1970 1980 1990 2000 Change in Population (in millions) 1.9 1.4 -0.1 2 3.1

Make a time-series graph showing the growth of New York City. What conclusions do you draw?


(The growth of New York City does not appear to be constant over time. There was a decrease in the population between 1970 and 1980.)


Mini-Lecture 2.4 Graphical Misrepresentations of Data Objective

1. Describe what can make a graph misleading or deceptive Examples

1. The data in the table below represent the historical life expectancies (in years) of residents of the United States. (Source: Source: National Center for Health Statistics, National Vital Statistics Reports, vol. 52, no. 3, Sept. 18, 2003. www.cdc.gov/nchs, accessed from http://www.infoplease.com/ipa/A0005148.html)

Year, x Life Expectancy, y 1950 68.2 1960 69.7 1970 70.8 1980 73.7 1990 75.4 2000 77.0

a. Construct a misleading time-series plot that indicates that the life expectancy has risen sharply over time.


b. Construct a time-series plot that is not misleading.

2. The National Survey of Student Engagement is a survey that (among other things) asked first year students at liberal arts colleges how much time they spend preparing for class each week. The results from the 2007 survey are summarized below. (Source: http://nsse.iub.edu/NSSE_2007_Annual_Report/docs/withhold/NSSE_2007_Annual_Report.pdf )

Hours 0 1-5 6-10 11-15 16-20 21-25 26-30 31-35 Percentage of 1st year students 0% 13% 25% 23% 18% 10% 6% 5%


a. Construct a pie chart that exaggerates the percentage of students who spend between 6 and 10 hours preparing for class each week.

b. Construct a pie chart that is not misleading.


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