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A PowerPoint Presentation Package to Accompany Applied Statistics in Business & Economics, 4th edition David P. Doane and Lori E. Seward Prepared by Lloyd R. Jaisingh McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Contents Chapter 3 Describing Data Visually 3.1 Stem-and-Leaf Displays and Dot Plots 3.2 Frequency Distributions and Histograms 3.3 Excel Charts 3.4 Line Charts 3.5 Bar Charts 3.6 Pie Charts 3.7 Scatter Plots 3.8 Tables 3.9 Deceptive Graphs 3-2 Chapter 3 Describing Data Visually Chapter Learning Objectives LO3-1: Make a stem-and-leaf or dot plot by hand or by computer. LO3-2: Create a frequency distribution for a data set. LO3-3: Make a histogram with appropriate bins. LO3-4: Identify skewness, modal classes, and outliers in a histogram. LO3-5: Make an effective line chart using Excel. 3-3 Chapter 3 Describing Data Visually Chapter Learning Objectives LO3-6: Know the rules for effective bar charts and pie charts. LO3-7: Make and interpret a scatter plot using Excel. LO3-8: Make simple tables and pivot tables. LO3-9: Recognize deceptive graphing techniques. 3-4 • Chapter 3 3.1 Stem-and-Leaf Displays and Dot Plots Methods of organizing, exploring and summarizing data include: - Visual (charts and graphs) provides insight into characteristics of a data set without using mathematics. - Numerical (statistics or tables) provides insight into characteristics of a data set using mathematics. 3-5 • Chapter 3 3.1 Stem-and-Leaf Displays and Dot Plots Begin with univariate data (a set of n observations on one variable) and consider the following: 3-6 • • • Measurement Chapter 3 • 3.1 Stem-and-Leaf Displays and Dot Plots Look at the data and visualize how they were collected and measured. Sorting (Example: Price/Earnings Ratios) Sort the data and then summarize in a graphical display. Here are the sorted P/E ratios (values from Table 3.2). 3-7 3.1 Stem-and-leaf Displays and Dot Plots Chapter 3 LO3-1 The type of graph you use to display your data is dependent on the type of data you have. Some charts are better suited for quantitative data, while others are better for displaying categorical data. LO3-1: Make a stem-and-leaf or dot plot by hand or by computer. Stem-and-Leaf Plot One simple way to visualize small data sets is a stem-and-leaf plot. The stem-and-leaf plot is a tool of exploratory data analysis (EDA) that seeks to reveal essential data features in an intuitive way. A stemand-leaf plot is basically a frequency tally, except that we use digits instead of tally marks. For two-digit or three-digit integer data, the stem is the tens digit of the data, and the leaf is the ones digit. 3-8 3.1 Stem-and-Leaf Displays and Dot Plots Chapter 3 LO3-1 For the 44 P/E ratios, the stem-and-leaf plot is given below. For example, the data values in the fourth stem are 31, 37, 37, 38. We always use equally spaced stems (even if some stems are empty). The stem-and-leaf can reveal central tendency (24 of the 44 P/E ratios were in the 10–19 stem) as well as dispersion (the range is from 7 to 59). In this illustration, the leaf digits have been sorted, although this is not necessary. The stem-and-leaf has the advantage that we can retrieve the raw data by concatenating a stem digit with each of its leaf digits. For example, the last stem has data values 50 and 59. 3-9 3.1 Stem-and-Leaf Displays and Dot Plots Chapter 3 LO3-1 Dot Plots • A dot plot is the simplest graphical display of n individual values of numerical data. - Easy to understand. - It reveals dispersion, central tendency, and the shape of the distribution. • Steps in Making a Dot Plot 1. Make a scale that covers the data range. 2. Mark the axes and label them. 3. Plot each data value as a dot above the scale at its approximate location. Note: If more than one data value lies at about the same axis location, the dots are stacked vertically. 3-10 • • • • 3.1 Stem-and-Leaf Displays and Dot Plots Chapter 3 LO3-1 The range is from 7 to 59. All but a few data values lie between 10 and 25. A typical “middle” data value would be around 17 or 18. The data are not symmetric due to a few large P/E ratios. 3-11 3.1 Stem-and-Leaf Displays and Dot Plots Chapter 3 LO3-1 Comparing Groups • A stacked dot plot compares two or more groups using a common X-axis scale. 3-12 LO3-2: Create a frequency distribution for a data set Chapter 3 LO3-2 3.2 Frequency Distributions and Histograms Bins and Bin Limits • A frequency distribution is a table formed by classifying n data values into k classes (bins). • Bin limits define the values to be included in each bin. Widths must all be the same except when we have open-ended bins. Frequencies are the number of observations within each bin. • • Express as relative frequencies (frequency divided by the total) or percentages (relative frequency times 100). 3-13 Constructing a Frequency Distribution Chapter 3 LO3-2 3.2 Frequency Distributions and Histograms - Herbert Sturges proposed the following rule: 3-14 Chapter 3 LO3-2 3.2 Frequency Distributions and Histograms 3-15 Chapter 3 LO3-2 3.2 Frequency Distributions and Histograms Histograms • A histogram is a graphical representation of a frequency distribution. Y-axis shows frequency within each bin. • A histogram is a bar chart. X-axis ticks shows end points of each bin. 3-16 LO3-3: Make a histogram with appropriate bins. • Chapter 3 LO3-3 3.2 Frequency Distributions and Histograms Consider 3 histograms for the P/E ratio data with different bin widths. What do they tell you? 3-17 Chapter 3 LO3-3 3.2 Frequency Distributions and Histograms LO3-3: Make a histogram with appropriate bins. • Choosing the number of bins and bin limits in creating histograms requires judgment. • One can use software programs to create histograms with different bins. These include software such as: Excel MegaStat Minitab • • • 3-18 LO3-3 Chapter 3 3.2 Frequency Distributions and Histograms Modal Class • A histogram bar that is higher than those on either side. • Unimodal – a single modal class. • Bimodal – two modal classes. • Multimodal – more than two modal classes. • Modal classes may be artifacts of the way bin limits are chosen. 3-19 LO3-4 LO3-4: Identify skewness, modes, and outliers in a histogram. Chapter 3 3.2 Frequency Distributions and Histograms Shape • A histogram may suggest the shape of the population. • It is influenced by the number of bins and bin limits. • Skewness – indicated by the direction of the longer tail of the histogram. Left-skewed – (negatively skewed) a longer left tail. Right-skewed – (positively skewed) a longer right tail. Symmetric – both tail areas are the same. 3-20 Chapter 3 LO3-4 3.2 Frequency Distributions and Histograms 3-21 Frequency Polygons and Ogives Chapter 3 3.2 Frequency Distributions and Histograms • A frequency polygon is a line graph that connects the midpoints of the histogram intervals, plus extra intervals at the beginning and end so that the line will touch the X-axis. • It serves the same purpose as a histogram, but is attractive when you need to compare two data sets (since more than one frequency polygon can be plotted on the same scale). • An ogive (pronounced “oh-jive”) is a line graph of the cumulative frequencies. • It is useful for finding percentiles or in comparing the shape of the sample with a known benchmark such as the normal distribution (that you will be seeing in the next chapter). 3-22 Chapter 3 3.2 Frequency Distributions and Histograms Frequency Polygons and Ogives 3-23 Chapter 3 3.3 Excel Charts This section describes how to use Excel to create charts. Please refer to the text. 3-24 3.4 Line Charts Chapter 3 LO3-5 LO3-5: Make an effective line chart using Excel. Simple Line Charts • Used to display a time series or spot trends, or to compare time periods. • Can display several variables at once. 3-25 3.4 Line Charts Simple Line Charts • Chapter 3 LO3-5 Two-scale line chart – used to compare variables that differ in magnitude or are measured in different units. 3-26 3.4 Line Charts Chapter 3 LO3-5 Log Scales • Arithmetic scale – distances on the Y-axis are proportional to the magnitude of the variable being displayed. • Logarithmic scale – (ratio scale) equal distances represent equal ratios. • Use a log scale for the vertical axis when data vary over a wide range, say, by more than an order of magnitude. • This will reveal more detail for smaller data values. 3-27 3.4 Line Charts Log Scales Chapter 3 LO3-5 A log scale is useful for time series data that might be expected to grow at a compound annual percentage rate (e.g., GDP, the national debt, or your future income). It reveals whether the quantity is growing at an increasing percent (concave upward), constant percent (straight line), or declining percent (concave downward) 3-28 3.5 Bar Charts LO3-6: Know the rules for effective bar charts and pie charts. Chapter 3 LO3-6 Simple Bar Charts • Most common way to display attribute data. - Bars represent categories or attributes. - Lengths of bars represent frequencies. 3-29 3.5 Bar Charts Pareto Charts • Special type of bar chart used in quality management to display the frequency of defects or errors of different types. • Categories are displayed in descending order of frequency. • Focus on significant few (i.e., few categories that account for most defects or errors). Chapter 3 LO3-6 3-30 Chapter 3 LO3-6 3.5 Bar Charts Stacked Bar Chart • Bar height is the sum of several subtotals. Areas may be compared by color to show patterns in the subgroups and total. 3-31 3.6 Pie Charts Chapter 3 LO3-6 LO3-6: Know the rules for effective bar charts and pie charts. An Oft-Abused Chart • • • • A pie chart can only convey a general idea of the data. Pie charts should be used to portray data which sum to a total (e.g., percent market shares). A pie chart should only have a few (i.e., 2 or 3) slices. Each slice can be labeled with data values or percents. 3-32 3.6 Pie Charts An Oft-Abused Chart • Chapter 3 LO3-6 Consider the following charts used to illustrate an article from the Wall Street Journal. Which type appears to be better? 3-33 3.6 Pie Charts Pie Chart Options • Chapter 3 LO3-6 Exploded and 3-D pie charts add strong visual impact. 3-34 3.7 Scatter Plots Chapter 3 LO3-7 LO3-7: Make and interpret a scatter plot using Excel. • Scatter plots can convey patterns in data pairs that would not be apparent from a table. Refer to the text for EXCEL outputs. 3-35 Chapter 3 3.8 Tables • Tables are the simplest form of data display. • A compound table is a table that contains time series data down the columns and variables across the rows. Example: School Expenditures • Arrangement of data is in rows and columns to enhance meaning. • The data can be viewed by focusing on the time pattern (down the columns) or by comparing the variables (across the rows). 3-36 Example: School Expenditures • • • Chapter 3 3.8 Tables Units of measure are stated in the footnote. Note merged headings to group columns. See text for “Tips for Effective Bar and Column Charts.” Tables”. 3-37 3.8 Tables Chapter 3 LO3-8 LO3-8: Make simple tables and Pivot tables Here are some tips for creating effective tables: 1. Keep the table simple, consistent with its purpose. Put summary tables in the main body of the written report and detailed tables in an appendix. 2. Display the data to be compared in columns rather than rows. 3. For presentation purposes, round off to three or four significant digits. 4. Physical table layout should guide the eye toward the comparison you wish to emphasize. 5. Row and column headings should be simple yet descriptive. 6. Within a column, use a consistent number of decimal digits. 3-38 Chapter 3 3.9 Deceptive Graphs LO3-9 LO3-9: Recognize deceptive graphing techniques. Error 1: Nonzero Origin • A nonzero origin will exaggerate the trend. Deceptive Correct 3-39 3.9 Deceptive Graphs Error 2: Elastic Graph Proportions • Chapter 3 LO3-9 Keep the aspect ratio (width/height) below 2.00 so as not to exaggerate the graph. By default, Excel uses an aspect ratio of 1.68. 3-40 3.9 Deceptive Graphs Chapter 3 LO3-9 Error 4: 3-D and Novelty Graphs • Can make trends appear to dwindle into the distance or loom towards you. 3-41 3.9 Deceptive Graphs Chapter 3 LO3-9 Error 5: 3-D and Rotated Graphs • Can make trends appear to dwindle into the distance or loom towards you. 3-42 3.9 Deceptive Graphs Error 8: Complex Graphs • Chapter 3 LO3-9 Avoid if possible. Keep your main objective in mind. Break graph into smaller parts. 3-43 3.9 Deceptive Graphs Error 11: Area Trick • Chapter 3 LO3-9 As figure height increases, so does width, distorting the graph. 3-44 3.9 Deceptive Graphs Chapter 3 LO3-9 • Other deceptive graphing techniques. • • • • • Error 3: Error 6: Error 7: Error 9: Error 10: Dramatic Title and Distracting Pictures Unclear Definitions or Scales Vague Sources Gratuitous Effects Estimated Data 3-45