Displaying Distributions - Qualitative Variables

Displaying Distributions - Qualitative VariablesLecture 12

Sections 4.3.1 - 4.3.2

Robb T. Koether

Hampden-Sydney College

Tue, Sep 13, 2011

Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Sep 13, 2011 1 / 24

Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs

5 How Not To Draw a Bar Graph

6 Assignment

7 Answers to Even-numbered Exercises


Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



Homework Review

Exercise 4.1, p. 219State what type of variable each of the following is. If a variable isquantitative, say whether it is discrete or continuous.

(a) Religious preference.Qualitative.

(b) Amount of milk in a glass.Quantitative continuous.

(c) Credit-card numbers.Qualitative.

(d) The number of students in a class of 35 who turn in a term paperon time.Quantitative discrete.


Homework Review

Exercise 4.1, p. 219State what type of variable each of the following is. If a variable isquantitative, say whether it is discrete or continuous.(a) Religious preference.

Qualitative.(b) Amount of milk in a glass.

Quantitative continuous.(c) Credit-card numbers.

Qualitative.(d) The number of students in a class of 35 who turn in a term paper

on time.Quantitative discrete.


Homework Review


Qualitative.

(b) Amount of milk in a glass.Quantitative continuous.




Homework Review







Homework Review



Quantitative continuous.




Homework Review







Homework Review




Qualitative.



Homework Review





on time.

Quantitative discrete.


Homework Review







Homework Review

Exercise 4.1, p. 219(e) The brand of personal computer purchased by a customer.

Qualitative.(f) The amount of fluid dispensed by a machine used to fill cups with

coffee.Quantitative continuous.


Homework Review


Qualitative.

(f) The amount of fluid dispensed by a machine used to fill cups withcoffee.Quantitative continuous.


Homework Review



coffee.

Quantitative continuous.


Homework Review



coffee.Quantitative continuous.


Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



Introduction

The two most basic characteristics of a sample that we areinterested in are averages and proportions.

How can we represent a proportion in a graph?How can we represent an average in a graph?What other characteristics might we want to represent in a graph?


Introduction

The two most basic characteristics of a sample that we areinterested in are averages and proportions.How can we represent a proportion in a graph?

How can we represent an average in a graph?What other characteristics might we want to represent in a graph?


Introduction

The two most basic characteristics of a sample that we areinterested in are averages and proportions.How can we represent a proportion in a graph?How can we represent an average in a graph?

What other characteristics might we want to represent in a graph?


Introduction

The two most basic characteristics of a sample that we areinterested in are averages and proportions.How can we represent a proportion in a graph?How can we represent an average in a graph?What other characteristics might we want to represent in a graph?


Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



Pie Charts

Definition (Pie chart)A pie chart is a display of qualitative data in which each category isrepresented by a slice of a pie. The size of each pie slice isproportional to the number of observations in that category.

Use the percentage associated with the category to compute thecentral angle of the pie slice.For example, 25% of 360◦ = 90◦.A pie chart facilitates the comparison of one category to the whole.


Pie Charts

25%

75%


Example

How was the weather in Farmville in January 2009?According to the National Weather Service:

Weather Conditions No. of DaysSunny 14Mostly Sunny 3Mostly Cloudy 3Cloudy 1Fog 0Rain 7Snow 3

Use Excel to draw a pie chart of the data.


http://www.wunderground.com/history/airport/KFVX/2009/1/3/MonthlyHistory.html

Example

How was the weather in Farmville in January 2010?According to the National Weather Service:

Weather Conditions No. of DaysSunny 9Mostly Sunny 10Mostly Cloudy 2Cloudy 0Fog 2Rain 6Snow 2

Use Excel to draw a pie chart of the data.


http://www.wunderground.com/history/airport/KFVX/2009/7/3/MonthlyHistory.html

Example

How did the Farmville weather in January 2009 compare to theFarmville weather in January 2010?It is not a good idea to try to compare the two pie charts.Instead, a bar graph should be used.


Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



Bar Graphs

Definition (Bar graph)A bar graph is a display of qualitative data in which each category isrepresented by a rectangle. The height of the rectangle is proportionalto the number of observations in that category.

The horizontal scale shows the categories.The vertical scale shows the counts or percentages.The horizontal/vertical orientation may be reversed.A bar graph facilitates the comparison of one category to another.


Example

How was the weather in Farmville in January 2009?Weather Conditions No. of DaysSunny 14Mostly Sunny 3Mostly Cloudy 3Cloudy 1Fog 0Rain 7Snow 3

Use Excel to draw a bar graph of the data.


Example

Now use a bar graph to compare the January 2009 weather to theJanuary 2010 weather.

Weather Conditions January JulyClear 14 9Mostly Sunny 3 10Mostly Cloudy 3 2Cloudy 1 0Fog 0 2Rain 7 6Snow 3 2

Use Excel to draw a bar graph of the data.


Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



How Not To Draw a Bar Graph

After the Republican debate last week, MSNBC conducted asurvey asking the viewers to tell which candidate they believe wonthe debate.The results were summarized in a bar graph.http://firstread.msnbc.msn.com/...

What is wrong with this bar graph?


http://firstread.msnbc.msn.com/_news/2011/09/07/7658608-who-do-you-think-won-the-republican-debate-at-the-reagan-library

Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



Assignment

HomeworkRead Section 4.3.1 - 4.3.2, pages 220 - 225.Let’s Do It! 4.3, 4.4, 4.5.Page 226, exercises 6 - 10.


Outline

1 Homework Review

2 Introduction

3 Pie Charts

4 Bar Graphs


6 Assignment



Answers to Even-numbered Exercises

Pag 226, Exercises 6, 8, 104.6 (a) Yes.

(b) 45%.(c)

Stayedthe

same

Improveda lot

Improvedsome

Don'tknow

60%

50%

40%

30%

20%

10%

0%

(d) Do the teachers agree that the students’ grades haveimproved? Did the students’ improvement depend onthe type of computer or the software?


Answers to Even-numbered Exercises

Pag 226, Exercises 6, 8, 104.8 NO!!! The categories do not add up to 100%.

4.10 (a) 69%.(b) 385.


Displaying Distributions - Qualitative Variables

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