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Quantitative Categorical

When looking at Data, we can describe it using graphs. The type of data tells us the type of graphs we can use. Here are examples of the different types of graphs:

Quantitative Categorical

Data that uses values from several possible categories.

Examples:

Data for which arithmetic operations, such

as ____________________ or

_____________________, makes sense.

Examples:

Histogram

Dot Plot

Box Plot

Stemplot

Bar Chart

Pie Chart

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Categorical Variables and Two Way Tables

A researcher suspects there is a relationship between people’s preferences in movies and their preferences in pizza. A random sample of 100 people produced the following results:

1. Find the totals for the table above.

2. What percent of the people who preferred Wolverine liked cheese pizza the best?

3. What percent of the people who preferred veggie pizza liked Finding Dory the best?

4. Calculate the conditional distributions in percents of favorite movie. What can you conclude?

Favorite Movie \ Pizza Meat Cheese VeggieThe Fault in Our Stars

WolverineFinding Dory

5. Calculate the conditional distributions in percents of favorite pizza. What can you conclude?

Favorite Movie \ Pizza Meat Cheese VeggieThe Fault in Our Stars

WolverineFinding Dory

6. Construct a segmented bar graph to show all the conditional distributions of favorite pizza among favorite movie.

Do you believe there is a relationship between people’s preferences in movie and their preference in pizza? If so, what is it?

Is this a causal relationship or could there be possible lurking variables to explain an association between pizza and movie preference? If yes, what are they?

Favorite Movie \ Pizza Meat Cheese VeggieThe Fault in Our Stars 5 7 13

Wolverine 20 8 5Finding Dory 8 22 12

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Mean Salaries

A business has two types of employees: managers and workers. Managers earn either $100,000 or $200,000 per year. Workers earn either $10,000 or $20,000 per year. The number of male and female managers at each salary level and the number of male and female workers at each salary level are given in the table below.

Managers WorkersMale Female Male Female

$100,000 80 20 $10,000 30 20$200,000 20 30 $20,000 20 80

Investigate the three statements below (see if they are true or false) and see if you can see what is happening.

1. The mean salary of female managers is $40,000 greater than that of male managers.

2. There are more females employed by this company than males.

3. The mean salary of females is greater than that of males for both managers and workers, indicating that the mean salary of female employees in general is greater than that of male employees in general.

Stem Plot and Dot Plot Practice

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A restaurant’s last 9 health scores are:

89, 94, 60, 78, 80, 82, 84, 81, and 92

Find the median, upper and lower quartiles, range, and the interquartile range.

Sketch a Stem plot Sketch a dot plot.

What is different about these two graphs?

How are they similar?

Why might these graphs not be good graphs for this data?

Histogram Practice

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1. Listed below are two sets of scores that are supposed to be heights (in inches) of randomly selected adult males. One of the sets consists of real heights actually obtained from randomly selected adult males, but the other set consists of numbers that were fabricated. Use your calculator to sketch a histogram for each data set, and based on your histograms choose the set of data that you believe to be false and justify your decision.

DATA SET A DATA SET B

70 73 70 72 70 73 70 72

71 73 71 67 71 66 74 76

68 72 67 72 68 75 67 68

71 73 72 70 71 77 66 69

72 68 71 71 72 67 77 75

71 73 69 73 66 76 76 77

71 66 77 67 73 74 69 67

Frequency Tables and Histograms

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Here is data representing the speeds of 31 vehicles on Peachtree Parkway recorded by an observer between 8:00 and 9:00 am on July 6, 2006.

40 48 54 36 35 47 64 31 23 44 37 63

59 32 26 45 43 50 53 34 42 54 60 58

31 44 51 55 39 40 50

Answer the usual questions about this data:

Who:

What:

When:

Where:

Why:

How:

By whom:

Fill in the frequency table below and then draw the histogram:

Speeds Frequency20 – 2526 – 31 32 – 37 38 – 43 44 – 49 50 – 55 56 – 61 62 – 67

Write a brief description of the histogram in the context of the problem

A.P. Statistics Review: Analyzing Quantitative Data

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Here are the weights (in pounds) of 20 steer on an experimental feed diet from a farm in Tuscaloosa, Alabama:

183 140 136 142 172 153 172 156 70 167192 166 113 171 178 159 129 112 135 174

1. Describe the data completely.

2. Make a stem plot of the data.

3. Why is a stem plot more appropriate for this data than a dot plot?

4. Completely describe the distribution of the variable in context.

5. Use your graphing calculator to make a histogram of the data using Zoom Stat. Sketch the graph below. How does this distribution appear different from the one shown in the stem plot? Why?

Here are the numbers of international airline passengers (in thousands) for the each month in 1954, starting with January:

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204 188 235 227 234 264 302 293 259 229 203 229

6. Draw a time plot of the data. Identify and major patterns present and give an explanation for the patterns.

7. The following back to back stem plot compares the percent change in population for the two regions of the United States (based on census figures from 1990 and 2000). The fastest growing states were Nevada and Arizona at 66% and 40% respectively. Write a few sentences describing the difference in the growth rates for the two regions of the United States.

NE/MW States S/W States

6 66554 4 033 0012 62 0011341 578

2100 1 001134444 99998876655 0 6999

4431 0 1

Box Plots and more…

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In a constant effort to improve service, Amazon.com asks its clients to rate their online shopping experience by giving it a rating from 1 star to 10 stars. A rating of 1 star represents a poor experience, and a rating of 10 stars represents an excellent experience. The ratings for one day last month are shown below:

The distribution above represents data. The distribution above is _______________.

a) Find the mean and median of the data set. b) Let’s also find the following information from our data: Use them to describe the distribution. Lower Quartile

Q2 (Median)Upper QuartileInterquartile Range

Outlier boundaries:

c) Create a Box Plot for this data

Another way to describe the data is to calculate the measures of spread.

d) Range:_________ What it tells us:

e) IQR:_______ What it tells us:

f) Standard Deviation:________ What it tells us:

Remember this example:89, 94, 60, 78, 80, 82, 84, 81, and 92.

Sketch a box-and-whisker plot and a modified box-and-whisker plot.

Poverty in Eastern States

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The poverty rates for states east of the Mississippi have been divided into northern and southern states, according to the geographic divisions used by the Census Bureau. Below is the data reported for these states in 1999.

Southern State Poverty Rate (%) Northern Poverty Rate (%)

Alabama 12.5 Connecticut 6.2Delaware 6.5 Illinois 7.8

Florida 9.0 Indiana 6.7Georgia 9.9 Maine 7.8

Kentucky 12.7 Massachusetts 6.7Maryland 6.1 Michigan 7.4

Mississippi 16.0 New Hampshire 4.3North Carolina 9.0 New Jersey 6.3South Carolina 10.7 New York 11.5

Tennessee 10.3 Ohio 7.8Virginia 7.0 Pennsylvania 7.8

West Virginia 13.9 Rhode Island 8.9Vermont 6.3

Wisconsin 5.6

Create side-by-side boxplots of the two region’s poverty rates on your calculator and draw an accurate graph of your display below. Be sure to label completely. Write a brief comparison (shape, center & spread) of the two displays.

Calories in Cereal: Consider the question: How many calories are in a bowl of breakfast cereal? Refer to the table below giving the calorie count for 22 different cereals to answer the

questions below:

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Cereal Calories Cereal CaloriesKellogg’s All Bran 74 Kixx 109Quaker 100% Natural 121 Nabisco Bran 74Bran Flakes 88 Total Raisin Bran 89Fruited Fiber 86 Wheaties 105Honey Smacks 113 Rice Krispies 110Quaker Puffed Rice 111 Fruit Loops 113Product 19 112 Kellogg’s Raisin Bran 89Post Raisin Bran 84 Frosted Mini-Wheats 99Mueslix Bran 87 Life 104Total Corn Flakes 110 Honey Nut 102Cheerios 106 Apple Jacks 116

1. Using your calculator, create a boxplot of the calories in cereal. Sketch the boxplot below and describe the distribution you see. What does the graph seem to tell you about the calories in cereal?

2. Create a histogram of the calories in cereal using a class size of 5. Sketch the histogram below. Describe the distribution of calories in cereal as it appears in the histogram. Is there anything that is evident from the histogram that is not evident in the boxplot and vice versa?

3. Look at the 5-number summary as well as the mean and standard deviation of the calories. Write a short description of the distribution, the center, and the variation in the number of calories in cereal.

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Chapter 1 Free Response Practice (1997 #1)

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation.

Age Data

Age 1900 20005 0.121 0.06615 0.344 0.20925 0.540 0.34435 0.700 0.48045 0.822 0.64355 0.906 0.78165 0.959 0.870

(a) Approximate the median age for each distribution.

(b) Approximate the interquartile range for each distribution.

(c) Using the results from parts a and b, write a sentence or two for a history textbook comparing the age distributions for the years 1900 and 2000.

The table of data provides the cumulative proportions for the United States population at selected ages for the years 1900 and 200 (projected). For example, 0.344 or 34.4 percent of the population was at or under age 15 in 1900, while only 0.209 or 20.9 percent will be at or under age 15 in the year 2000. The graph below shows the cumulative proportions plotted against age for the years 1900 and 2000(projected). The data and graph are to be used to compare the age distribution for the year 1900 with the projected age distribution for the year 2000.

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