Pie Charts and Pareto Charts • How to Graph and Interpret Paired Data Sets Using Scatter Plots and Time Series Charts

Elementary Statistics: Picturing The World Sixth Edition

2.1 Frequency Distributions and Their Graphs 2.2 More Graphs and Displays 2.3 Measures of Central Tendency 2.4 Measures of Variation 2.5 Measures of Position

• How to graph and interpret quantitative data using stem-and-leaf plots and dot plots • How to graph and interpret qualitative data using pie charts and Pareto charts • How to graph and interpret paired data sets using scatter plots and time series charts

Stem-and-leaf plot • Each number is separated into a stem and a leaf. • Similar to a histogram. • Still contains original data values. Data: 21, 25, 25, 26, 27, 28, 30, 36, 36, 45

The following are the numbers of text messages sent last month by the cellular phone users on one floor of a college dormitory. Display the data in a stem-and-leaf plot.

155 159 144 129 105 145 126 116 130 114 122 112 112 142 126 118 118 108 122 121 109 140 126 119 113 117 118 109 109 119 139 139 122 78 133 126 123 145 121 134 124 119 132 133 124 129 112 126 148 147 blank blank blank blank blank blank blank blank blank blank • The data entries go from a low of 78 to a high of 159. • Use the rightmost digit as the leaf. – For instance, 78 = 7 | 8 and 159 = 15 | 9 • List the stems, 7 to 15, to the left of a vertical line. • For each data entry, list a leaf to the right of its stem. Copyright © 2015, 2012, 2009 Pearson Education, Inc. All Rights Reserved Example: Constructing a Stem-and- Leaf Plot (3 of 3)

From the display, you can conclude that more than 50% of the cellular phone users sent between 110 and 130 text messages.

Dot plot • Each data entry is plotted, using a point, above a horizontal axis Data: 21, 25, 25, 26, 27, 28, 30, 36, 36, 45

• So that each data entry is included in the dot plot, the horizontal axis should include numbers between 70 and 160. • To represent a data entry, plot a point above the entry's position on the axis. • If an entry is repeated, plot another point above the previous point.

From the dot plot, you can see that most values cluster between 105 and 148 and the value that occurs the most is 126. You can also see that 78 is an unusual data value.

Pie Chart • A circle is divided into sectors that represent categories. • The area of each sector is proportional to the frequency of each category.

Copyright © 2015, 2012, 2009 Pearson Education, Inc. All Rights Reserved Example: Constructing a Pie Chart (1 of 5) The numbers of earned degrees conferred (in thousands) in 2007 are shown in the table. Use a pie chart to organize the data. (Source: U.S. National Center for Educational Statistics)

Type of degree Number (thousands) Associate’s 728 Bachelor’s 1525 Master’s 604 First professional 90 Doctoral 60

• Construct the pie chart using the central angle that corresponds to each category. – To find the central angle, multiply 360º by the category's relative frequency. – For example, the central angle for cars is 360(0.24) ≈ 86º

Relative Type of degree Frequency, f Central angle frequency Associate’s 728 0.24 360º(0.24) ≈ 86º Bachelor’s 1525 0.51 360º(0.51) ≈ 184º Master’s 604 0.20 360º(0.20) ≈ 72º First professional 90 0.03 360º(0.03) ≈ 11º Doctoral 60 0.02 360º(0.02) ≈ 7º

Relative Central Types of degree frequency angle Associate’s 0.24 86º Bachelor’s 0.51 184º Master’s 0.20 72º First professional 0.03 11º Doctoral 0.02 7º

From the pie chart, you can see that almost one-half of the degrees conferred in 2011 were bachelor’s degrees.

Pareto Chart • A vertical bar graph in which the height of each bar represents frequency or relative frequency. • The bars are positioned in order of decreasing height, with the tallest bar positioned at the left.

In a recent year, the retail industry lost $36.5 billion in inventory shrinkage. Inventory shrinkage is the loss of inventory through breakage, pilferage, shoplifting, and so on. The causes of the inventory shrinkage are administrative error ($5.4 billion), employee theft ($15.9 billion), shoplifting ($12.7 billion), and vendor fraud ($1.4 billion). Use a Pareto chart to organize this data. (Source: National Retail Federation and Center for Retailing Education, University of Florida)

Cause $ (billion) Admin. error 5.4 Employee 15.9 theft Shoplifting 12.7 Vendor fraud 1.4

From the graph, it is easy to see that the causes of inventory shrinkage that should be addressed first are employee theft and shoplifting.

Copyright © 2015, 2012, 2009 Pearson Education, Inc. All Rights Reserved Graphing Paired Data Sets (1 of 2) Paired Data Sets • Each entry in one data set corresponds to one entry in a second data set. • Graph using a scatter plot. – The ordered pairs are graphed as points in a coordinate plane. – Used to show the relationship between two quantitative variables.

The British statistician Ronald Fisher introduced a famous data set called Fisher's Iris data set. This data set describes various physical characteristics, such as petal length and petal width (in millimeters), for three species of iris. The petal lengths form the first data set and the petal widths form the second data set. (Source: Fisher, R. A., 1936)

As the petal length increases, what tends to happen to the petal width?

Interpretation From the scatter plot, you can see that as the petal length increases, the petal width also tends to increase.

Time Series • Data set is composed of quantitative entries taken at regular intervals over a period of time. – e.g., The amount of precipitation measured each day for one month. • Use a time series chart to graph.

Copyright © 2015, 2012, 2009 Pearson Education, Inc. All Rights Reserved Example: Constructing a Time Series Chart (1 of 3) Subscribers Average bill The table lists the number of cellular Year (in millions) (in dollars) telephone subscribers (in millions) 1998 69.2 39.43 for the years 1998 through 2008. Construct a time series chart for the 1999 86.0 41.24 number of cellular subscribers. 2000 109.5 45.27 (Source: Cellular Telecommunication & 2001 128.4 47.37 Internet Association) 2002 140.8 48.40 2003 158.7 49.91 2004 182.1 50.64 2005 207.9 49.98 2006 233.0 50.56

2007 255.4 49.79 2008 270.3 50.07

Copyright © 2015, 2012, 2009 Pearson Education, Inc. All Rights Reserved Example: Constructing a Time Series Chart (2 of 3) Subscribers Average bill Year (in millions) (in dollars) • Let the horizontal axis represent the 1998 69.2 39.43 years. 1999 86.0 41.24 • Let the vertical axis represent the 2000 109.5 45.27 number of subscribers (in millions). 2001 128.4 47.37 • Plot the paired data and connect 2002 140.8 48.40 them with line segments. 2003 158.7 49.91 2004 182.1 50.64 2005 207.9 49.98 2006 233.0 50.56

2007 255.4 49.79 2008 270.3 50.07

Copyright © 2015, 2012, 2009 Pearson Education, Inc. All Rights Reserved Example: Constructing a Time Series Chart (3 of 3) Subscribers Average bill Year (in millions) (in dollars) 1998 69.2 39.43 1999 86.0 41.24 2000 109.5 45.27 2001 128.4 47.37 2002 140.8 48.40 2003 158.7 49.91 2004 182.1 50.64 The graph shows that the number of 2005 207.9 49.98 subscribers has been increasing since 2006 233.0 50.56 1998, with greater increases recently. 2007 255.4 49.79 2008 270.3 50.07

• Graphed and interpreted quantitative data using stem- and-leaf plots and dot plots • Graphed and interpreted qualitative data using pie charts and Pareto charts • Graphed and interpreted paired data sets using scatter plots and time series charts