1. McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. A PowerPoint Presentation Package to Accompany Applied Statistics in Business & Economics, 4 th edition David P. Doane and Lori E. Seward Prepared by Lloyd R. Jaisingh

2. 3-2 Describing Data Visually Chapter Contents 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 Chapter 3

3. 3-3 Chapter Learning Objectives LO3-1 LO3-1 Make a stem-and-leaf or dot plot by hand or by computer. LO3-2 LO3-2 Create a frequency distribution for a data set. LO3-3 LO3-3 Make a histogram with appropriate bins. LO3-4 LO3-4 Identify skewness, modal classes, and outliers in a histogram. LO3-5 LO3-5 Make an effective line chart using Excel. LO3-6 LO3-6 Know the rules for effective bar charts and pie charts. LO3-7 LO3-7 Make and interpret a scatter plot using Excel. LO3-8 LO3-8 Make simple tables and pivot tables. LO3-9 LO3-9 Recognize deceptive graphing techniques. Chapter 3 Describing Data Visually

4. 3-4 Methods of organizing, exploring and summarizing data include.Methods of organizing, exploring and summarizing data include. Visual - Visual (charts and graphs) provides insight into characteristics of a data set without using mathematics. Numerical - Numerical (statistics or tables) provides insight into characteristics of a data set using mathematics. Chapter 3 3.1 Stem-and-leaf Displays and Dot Plots

5. 3-5 Begin with univariate data (a set of n observations on one variable) and consider the following:Begin with univariate data (a set of n observations on one variable) and consider the following: Chapter 3 3.1 Stem-and-leaf Displays and Dot Plots

6. 3-6 Sorting (Example: Price/Earnings Ratios) Sorting (Example: Price/Earnings Ratios) Measurement Measurement Look at the data and visualize how it was collected and measured. Sort the data and then summarize in a graphical display. Here are the sorted P/E ratios (values from Table 3.2). Chapter 3 3.1 Stem-and-leaf Displays and Dot Plots

7. 3-7 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. 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 stem- and-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. Chapter 3 Stem-and-Leaf Plot LO3-1: Make a stem-and-leaf or dot plot by hand or by computer. LO3-1 3.1 Stem-and-leaf Displays and Dot Plots

8. 3-8 For the 44 P/E ratios, the stem-and-leaf plot is given below. Chapter 3 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. LO3-1 3.1 Stem-and-leaf Displays and Dot Plots

9. 3-9 Steps in Making a Dot PlotSteps in Making a Dot Plot A dot plot is the simplest graphical display of n individual values of numerical data. - Easy to understand - Not good for large samples (e.g., > 5,000).. 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 piled up vertically. Chapter 3 LO3-1: Make a dot plot by hand or by computer Methods of organizing, exploring and summarizing data include:Methods of organizing, exploring and summarizing data include: -Visual -Visual (charts and graphs) provides insight into characteristics of a data set without using mathematics. -Numerical -Numerical (statistics or tables) provides insight into characteristics of a data set using mathematics. LO3-1 3.1 Stem-and-leaf Displays and Dot Plots

10. 3-10 Range of data shows dispersion.Range of data shows dispersion. Clustering shows central tendency.Clustering shows central tendency. Chapter 3LO3-1 3.1 Stem-and-leaf Displays and Dot Plots

11. 3-11 Bins and Bin Limits frequency distributionA frequency distribution is a table formed by classifying n data values into k classes (bins). Bin limitsBin limits define the values to be included in each bin. Widths must all be the same. FrequenciesFrequencies are the number of observations within each bin. relative frequencies percentagesExpress as relative frequencies (frequency divided by the total) or percentages (relative frequency times 100). Chapter 3 3.2 Frequency Distributions and Histograms LO3-2: Create a Frequency Distribution for a Data Set. LO3-2

12. 3-12 A histogram is a graphical representation of a frequency distributionA histogram is a graphical representation of a frequency distribution. A histogram is a bar chart.A histogram is a bar chart. Y-axis shows frequency within each bin Y-axis shows frequency within each bin. X-axis ticks shows end points of each bin. One can use appropriate technology to construct histograms Chapter 3Histograms LO3-3: Make a histogram with appropriate bins. LO3-3 3.2 Frequency Distributions and Histograms

13. 3-13 Chapter 3 LO3-4: Identify skewness, modes, and outliers in a histogram. LO3-4 3.2 Frequency Distributions and Histograms

14. 3-14 Chapter 3 Frequency Polygons and Ogives 3.3 EXCEL CHARTS This section describes how to use Excel to create charts. Refer to the text. 3.2 Frequency Distributions and Histograms

15. 3-15 Used to display a time series or spot trends, or to compare time periods.Used to display a time series or spot trends, or to compare time periods. Can display several variables at once.Can display several variables at once. Simple Line Charts Simple Line Charts Chapter 3 LO3-5: Make an effective line chart using Excel. 3.4 Line Charts LO3-5

16. 3-16 Log Scales Log Scales 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) Chapter 3 3.4 Line Charts LO3-5

17. 3-17 Most common way to display attribute data. - Bars represent categories or attributes. - Lengths of bars represent frequencies. Simple Bar Charts Simple Bar Charts Chapter 3 3.5 Bar Charts LO3-6: Know the rules for effective bar charts and pie charts. LO3-6

18. 3-18 Special type of bar chart used in quality management to display the frequency of defects or errors of different types.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.Categories are displayed in descending order of frequency. Focus on significant few (i.e., few categories that account for most defects or errors).Focus on significant few (i.e., few categories that account for most defects or errors). Pareto Charts Pareto Charts Chapter 3 3.5 Bar Charts LO3-6

19. 3-19 A pie chart can only convey a general idea of the data.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).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.A pie chart should only have a few (i.e., 2 or 3) slices. Each slice should be labeled with data values or percents.Each slice should be labeled with data values or percents. An Oft-Abused Chart An Oft-Abused Chart Chapter 3 3.6 Pie Charts LO3-6: Know the rules for effective bar charts and pie charts. LO3-6

20. 3-20 Scatter plots can convey patterns in data pairs that would not be apparent from a table. Scatter plots can convey patterns in data pairs that would not be apparent from a table. Chapter 3 3.7 Scatter Plots LO3-7: Make an interpret a scatter plot using Excel. LO3-7

21. 3-21 Chapter 3 3.8 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. LO3-8: Make simple tables and Pivot tables. TablesTables are the simplest form of data display. compound tableA compound table is a table that contains time series data down the columns and variables across the rows. LO3-8

22. 3-22 Chapter 3 3.9 Deceptive Graphs LO3-9: Recognize deceptive graphing techniques. Error 1: Nonzero Origin Error 2: Elastic Graph Proportions Error 3: Dramatic Title Error 4: Distracting Pictures Error 5: Authority Figures Error 6: 3-D and Rotated Graphs Error 7: Missing Axis Demarcations Error 8: Missing Measurement Units or Definitions Error 9: Vague Source Error 10: Complex Graphs Error 11: Gratuitous Effects Error 12: Estimated Data Error 13: Area Trick LO3-9