A survey of 200 adults in the U.S. found that 76% regularly wear seatbelts while driving. True or false: 76% is a parameter.

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1 A survey of 200 adults in the U.S. found that 76% regularly wear seatbelts while driving. True or false: 76% is a parameter. A. True B. False Slide 1-1 Copyright 2010 Pearson Education, Inc.

2 True or false: The checking account numbers of customers at a bank represent quantitative data. A. True B. False Slide 1-2 Copyright 2010 Pearson Education, Inc.

3 Determine whether the quantitative variable is continuous or discrete. The time (in minutes) required for a student to complete a quiz. A. Continuous B. Discrete Slide 1-3 Copyright 2010 Pearson Education, Inc.

4 Identify the variable s level of measurement: Consumer Reports ratings (Best Buy, Recommended, Not Recommended). A. Nominal B. Ordinal C. Interval D. Ratio Slide 1-4 Copyright 2010 Pearson Education, Inc.

5 Determine whether the study depicts an observational study or an experiment: Two sections of statistics are taught by the same teacher. One section uses MyStatLab; the other section does not. At the end of the semester grades in the two sections are compared. A. Observational study B. Experiment Slide 1-5 Copyright 2010 Pearson Education, Inc.

6 Identify the type of sampling used: Students at a university are classified according to major. The administration randomly selects five majors. All students majoring in those five areas are surveyed. A. Simple random sample B. Stratified sample C. Cluster sample D. Systematic sample Slide 1-6 Copyright 2010 Pearson Education, Inc.

7 Chapter 32 Organizing and Summarizing Data Statistics: The only science that enables different experts using the same figures to draw different conclusions. Evan Esar 2010 Pearson Prentice Hall. All rights reserved

8 A lists each category of data and the number of occurrences for each category of data Pearson Prentice Hall. All rights reserved 2-8

9 When data is collected from a survey or designed experiment, they must be organized into a manageable form. Data that is not organized is referred to as. Ways to Organize Data 2010 Pearson Prentice Hall. All rights reserved 2-9

10 The is the proportion (or percent) of observations within a category and is found using the formula: relative frequency frequency sum of all frequencies A distribution lists the relative frequency of each category of data Pearson Prentice Hall. All rights reserved 2-10

11 EXAMPLE Organizing Qualitative Data into a Frequency Distribution The data on the next slide represent the color of M&Ms in a bag of plain M&Ms. Construct a frequency distribution of the color of plain M&Ms Pearson Prentice Hall. All rights reserved 2-11

12 Relative Frequency 2010 Pearson Prentice Hall. All rights reserved 2-12

13 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 Pearson Prentice Hall. All rights reserved 2-13

14 2010 Pearson Prentice Hall. All rights reserved 2-14

15 Relative Frequency Marital Status in 1990 vs Never married Married Widowed Divorced Marital Status 2010 Pearson Prentice Hall. All rights reserved 2-15

16 A 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 Pearson Prentice Hall. All rights reserved 2-16

17 EXAMPLE Constructing a Pie Chart The following data represent the marital status (in millions) of U.S. residents 18 years of age or older in Draw a pie chart of the data. Marital Status Frequency Never married 55.3 Married Widowed 13.9 Divorced Pearson Prentice Hall. All rights reserved 2-17

18 EXAMPLE 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 Data based on results reported by the United States Bureau of the Census Pearson Prentice Hall. All rights reserved 2-18

19 2010 Pearson Prentice Hall. All rights reserved 2-19

20 A 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 Pearson Prentice Hall. All rights reserved 2-20

21 2010 Pearson Prentice Hall. All rights reserved 2-21

22 2010 Pearson Prentice Hall. All rights reserved 2-22

23 Categories of data are created for continuous data using intervals of numbers called Pearson Prentice Hall. All rights reserved 2-23

24 The following data represents the number of persons aged who are currently work disabled. Age Number (in thousands) , , , ,108 The of a class is the smallest value within the class while the of a class is the largest 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 the first class is 34. The is the difference between consecutive lower class limits. The class width of the data given above is Pearson Prentice Hall. All rights reserved 2-24

25 EXAMPLE 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. Source: Ladonna Hansen, Park Curator 2010 Pearson Prentice Hall. All rights reserved 2-25

26 The smallest data value is 672 and the largest data value is 738. We will create the classes so that the lower class limit of the first class is 670 and the class width is 10 and obtain the following classes: 2010 Pearson Prentice Hall. All rights reserved 2-26

27 2010 Pearson Prentice Hall. All rights reserved 2-27

28 A uses digits to the left of the rightmost digit to form the. Each rightmost digit forms a. For example, a data value of 147 would have 14 as the stem and 7 as the leaf Pearson Prentice Hall. All rights reserved 2-28

29 EXAMPLE Constructing a Stem-and-Leaf Plot 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, Pearson Prentice Hall. All rights reserved 2-29

30 State Unemployment Rate State Unemployment Rate 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 5.2 Colorado 5.1 Michigan 8.5 Rhode Island 7.5 Conn 5.4 Minnesota 5.3 South Carolina 6.2 Delaware 4.2 Mississippi 6.9 South Dakota 2.8 Dist Col 6.4 Missouri 5.7 Tenn 6.5 Florida 5.5 Montana 4.1 Texas 4.4 Georgia 5.7 Nebraska 3.3 Utah 3.2 Hawaii 3.8 Nevada 6.4 Vermont 4.7 Idaho 3.8 New Hamp 4.0 Virginia 4.0 Illinois 6.8 New Jersey 5.3 Washington 5.5 Indiana 5.8 New Mexico 3.9 W. Virginia 5.3 Iowa 4.0 New York 5.3 Wisconsin 4.6 Kansas 4.3 North Carolina 6.0 Wyoming Pearson Prentice Hall. All rights reserved

31 2010 Pearson Prentice Hall. All rights reserved 2-31

32 A is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed Pearson Prentice Hall. All rights reserved 2-32

33 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 Pearson Prentice Hall. All rights reserved 2-33

34 2010 Pearson Prentice Hall. All rights reserved 2-34

35 EXAMPLE Identifying the Shape of the Distribution Identify the shape of the following histogram which represents the time between eruptions at Old Faithful Pearson Prentice Hall. All rights reserved 2-35

36 The is found by adding consecutive lower class limits and dividing the result by 2. A is drawn by plotting a point above each class midpoint on a horizontal axis at a height equal to the frequency of the class. After the points for each class are plotted, draw straight lines between consecutive points Pearson Prentice Hall. All rights reserved 2-36

37 Time between Eruptions (seconds) Class Midpoint Frequency Relative Frequency Pearson Prentice Hall. All rights reserved 2-37

38 Frequency Frequency Polygon 12 Time between Eruptions Time (seconds) 2010 Pearson Prentice Hall. All rights reserved 2-38

39 Relative Frequency Frequency Polygon 0.3 Time between Eruptions Time (seconds) 2010 Pearson Prentice Hall. All rights reserved 2-39

40 A displays the aggregate frequency of the category. In other words, for discrete data, it displays the total number of observations less than or equal to the category. For continuous data, it displays the total number of observations less than or equal to the upper class limit of a class. A displays the aggregate proportion (or percent) of observations less than or equal to the category Pearson Prentice Hall. All rights reserved 2-40

41 2010 Pearson Prentice Hall. All rights reserved 2-41

42 An is a graph that represents the cumulative frequency or cumulative relative frequency for the class. It is constructed by plotting points whose x-coordinates are the upper class limits and whose y-coordinates are the cumulative frequencies or cumulative relative frequencies. After the points for each class are plotted, draw straight lines between consecutive points. An additional line segment is drawn connecting the upper limit of the class that would preceed the first class (if it existed) Pearson Prentice Hall. All rights reserved 2-42

43 Cumulative Frequency Frequency Ogive Time between Eruptions Time (seconds) 2010 Pearson Prentice Hall. All rights reserved 2-43

44 Cumulative Relative Frequency Relative Frequency Ogive Time between Eruptions Time (seconds) 2010 Pearson Prentice Hall. All rights reserved 2-44

45 If the value of a variable is measured at different points in time, the data is referred to as. A is obtained by plotting the time in which a variable is measured on the horizontal axis and the corresponding value of the variable on the vertical axis. Lines are then drawn connecting the points Pearson Prentice Hall. All rights reserved 2-45

46 The data to the right shows the closing prices of the Dow Jones Industrial Average for the years Year Closing Value , , , , Pearson Prentice Hall. All rights reserved 2-46

47 Closing Value Dow Jones Industrial Average ( ) Year 2010 Pearson Prentice Hall. All rights reserved 2-47

48 EXAMPLE Misrepresentation of Data (a) The data in the table to the right represent the historical life expectancies (in years) of residents of the United States. (a)construct a misleading time series graph that implies that life expectancies have risen sharply. (b)construct a time series graph that is not misleading. Year, x Life Expectancy, y Source: National Center for Health Statistics (b) 2010 Pearson Prentice Hall. All rights reserved 2-48

49 EXAMPLE Misrepresentation of Data 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 to the right. (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. Hours Relative Frequency Source: ocs/withhold/nsse_2007_annual_report.pdf 2010 Pearson Prentice Hall. All rights reserved 2-49

50 (a) 2010 Pearson Prentice Hall. All rights reserved 2-50

51 (b) 2010 Pearson Prentice Hall. All rights reserved 2-51

52 Guidelines for Constructing Good Graphics Title and label the graphic axes clearly, providing explanations, if needed. Include units of measurement and a data source when appropriate. Avoid distortion. Never lie about the data. Minimize the amount of white space in the graph. Use the available space to let the data stand out. If scales are truncated, be sure to clearly indicate this to the reader. Avoid clutter, such as excessive gridlines and unnecessary backgrounds or pictures. Don t distract the reader. Avoid three dimensions. Three-dimensional charts may look nice, but they distract the reader and often lead to misinterpretation of the graphic. Do not use more than one design in the same graphic. Sometimes graphs use a different design in one portion of the graph to draw attention to that area. Don t try to force the reader to any specific part of the graph. Let the data speak for themselves. Avoid relative graphs that are devoid of data or scales Pearson Prentice Hall. All rights reserved 2-52