Displaying Distributions - Qualitative Variables

Transcription

1 Displaying Distributions - Qualitative Variables Lecture 12 Sections Robb T. Koether Hampden-Sydney College Tue, Feb 2, 2010 Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

2 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

3 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

4 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, say whether it is discrete or continuous. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

5 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, say whether it is discrete or continuous. (a) Religious preference. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

6 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, say whether it is discrete or continuous. (a) Religious preference. Qualitative. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

7 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, say whether it is discrete or continuous. (a) Religious preference. Qualitative. (b) Amount of milk in a glass. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

8 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, say whether it is discrete or continuous. (a) Religious preference. Qualitative. (b) Amount of milk in a glass. Quantitative continuous. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

9 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, say whether it is discrete or continuous. (a) Religious preference. Qualitative. (b) Amount of milk in a glass. Quantitative continuous. (c) Credit-card numbers. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

10 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

11 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

12 Homework Review Exercise 4.1, p. 219 State what type of variable each of the following is. If a variable is quantitative, 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

13 Homework Review Exercise 4.1, p. 219 (e) The brand of personal computer purchased by a customer. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

14 Homework Review Exercise 4.1, p. 219 (e) The brand of personal computer purchased by a customer. Qualitative. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

15 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

16 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

17 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

18 Introduction The two most basic characteristics of a sample that we are interested in are averages and proportions. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

19 Introduction The two most basic characteristics of a sample that we are interested in are averages and proportions. How can we represent a proportion in a graph? Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

20 Introduction The two most basic characteristics of a sample that we are interested in are averages and proportions. How can we represent a proportion in a graph? How can we represent an average in a graph? Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

21 Introduction The two most basic characteristics of a sample that we are interested 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? Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

22 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

23 Pie Charts Definition (Pie chart) A pie chart is a display of qualitative data in which each category is represented by a slice of a pie. The size of each pie slice is proportional to the number of observations in that category. Use the percentage associated with the category to compute the central angle of the pie slice. For example, 25% of 360 = 90. A pie chart facilitates the comparison of one category to the whole. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

24 Pie Charts 25% 75% Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

25 Example How was the weather in Farmville in January 2009? According to the National Weather Service: Weather Conditions No. of Days Sunny 14 Mostly Sunny 3 Mostly Cloudy 3 Cloudy 1 Fog 0 Rain 7 Snow 3 Use Excel to draw a pie chart of the data. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

26 Example How was the weather in Farmville in January 2010? According to the National Weather Service: Weather Conditions No. of Days Sunny 9 Mostly Sunny 10 Mostly Cloudy 2 Cloudy 0 Fog 2 Rain 6 Snow 2 Use Excel to draw a pie chart of the data. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

27 Example How did the Farmville weather in January 2009 compare to the Farmville 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

28 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

29 Bar Graphs Definition (Bar graph) A bar graph is a display of qualitative data in which each category is represented by a rectangle. The height of the rectangle is proportional to 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. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

30 Example How was the weather in Farmville in January 2009? Weather Conditions No. of Days Sunny 14 Mostly Sunny 3 Mostly Cloudy 3 Cloudy 1 Fog 0 Rain 7 Snow 3 Use Excel to draw a bar graph of the data. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

31 Example Now use a bar graph to compare the January 2009 weather to the January 2010 weather. Weather Conditions January July Clear 14 9 Mostly Sunny 3 10 Mostly Cloudy 3 2 Cloudy 1 0 Fog 0 2 Rain 7 6 Snow 3 2 Use Excel to draw a bar graph of the data. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

32 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

33 Assignment Homework Read Section , pages Let s Do It! 4.3, 4.4, 4.5. Page 226, exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

34 Outline 1 Homework Review 2 Introduction 3 Pie Charts 4 Bar Graphs 5 Assignment 6 Answers to Even-numbered Exercises Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

35 Answers to Even-numbered Exercises Pag 226, Exercises 6, 8, (a) Yes. (b) 45%. (c) 60% 50% 40% 30% 20% 10% 0% Stayed the same Improved some Improved a lot Don't know (d) Do the teachers agree that the students grades have improved? Did the students improvement depend on the type of computer or the software? Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22

36 Answers to Even-numbered Exercises Pag 226, Exercises 6, 8, NO!!! The categories do not add up to 100% (a) 69%. (b) 385. Robb T. Koether (Hampden-Sydney College)Displaying Distributions - Qualitative Variables Tue, Feb 2, / 22