McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.

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Applied Statistics in Business & Applied Statistics in Business & Economics, Economics, 44thth edition edition

David P. Doane and Lori E. Seward David P. Doane and Lori E. Seward

Prepared by Lloyd R. Jaisingh Prepared by Lloyd R. Jaisingh

3-2

Describing Data Visually Describing Data Visually

Chapter ContentsChapter 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

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Chapter Learning Objectives Chapter Learning Objectives

LO3-1LO3-1 Make a stem-and-leaf or dot plot by hand or by computer.

LO3-2LO3-2 Create a frequency distribution for a data set.

LO3-3LO3-3 Make a histogram with appropriate bins.

LO3-4LO3-4 Identify skewness, modal classes, and outliers in a histogram.

LO3-5LO3-5 Make an effective line chart using Excel.

LO3-6LO3-6 Know the rules for effective bar charts and pie charts.

LO3-7LO3-7 Make and interpret a scatter plot using Excel.

LO3-8LO3-8 Make simple tables and pivot tables.

LO3-9LO3-9 Recognize deceptive graphing techniques.

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Describing Data Visually Describing Data Visually

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• Methods of organizing, exploring and summarizing data include.Methods of organizing, exploring and summarizing data include.

- VisualVisual (charts and graphs) provides insight into characteristics of a data set without using mathematics.

- NumericalNumerical (statistics or tables) provides insight into characteristics of a data set using mathematics.

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3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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• Begin with univariate data (a set of Begin with univariate data (a set of nn observations on one variable) observations on one variable) and consider the following:and consider the following:

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3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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• Sorting Sorting (Example: Price/Earnings Ratios) (Example: Price/Earnings Ratios)

• MeasurementMeasurement

• 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).

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3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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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.

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Stem-and-Leaf Plot

LO3-1: LO3-1: Make a stem-and-leaf or dot plot by hand or by computer.Make a stem-and-leaf or dot plot by hand or by computer.

LO3-1LO3-1 3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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For the 44 P/E ratios, the stem-and-leaf plot is given below.

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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.

LO3-1LO3-1 3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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• 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.

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LO3-1:LO3-1: Make a dot plot by hand or by computerMake a dot plot by hand or by computer

• Methods of organizing, exploring and summarizing data include:Methods of organizing, exploring and summarizing data include:

- VisualVisual (charts and graphs) provides insight into characteristics of a data set without using mathematics.

- NumericalNumerical (statistics or tables) provides insight into characteristics of a data set using mathematics.

LO3-1LO3-1 3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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• Range of data shows Range of data shows dispersiondispersion. .

• Clustering shows Clustering shows central tendencycentral tendency. .

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LO3-1LO3-1 3.1 Stem-and-leaf Displays and Dot Plots3.1 Stem-and-leaf Displays and Dot Plots

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Bins and Bin LimitsBins and Bin Limits

• A frequency distributionfrequency 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.• Express as relative frequenciesrelative frequencies (frequency divided by the total) or percentagespercentages

(relative frequency times 100).

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3.2 Frequency Distributions and Histograms3.2 Frequency Distributions and Histograms

LO3-2: LO3-2: Create a Frequency Distribution for a Data Set.Create a Frequency Distribution for a Data Set.

LO3-2LO3-2

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• A A histogramhistogram is a graphical representation of a frequency distribution is a graphical representation of a frequency distribution.

• A A histogramhistogram is a bar chart. is a bar chart.

YY-axis shows frequency within each bin-axis shows frequency within each bin.

XX-axis ticks shows end points of each bin-axis ticks shows end points of each bin..

One can use appropriate technology to construct histogramsOne can use appropriate technology to construct histograms

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HistogramsHistograms

LO3-3: LO3-3: Make a histogram with appropriate bins.Make a histogram with appropriate bins.

LO3-3LO3-3 3.2 Frequency Distributions and Histograms3.2 Frequency Distributions and Histograms

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LO3-4: LO3-4: Identify skewness, modes, and outliers in a histogram.Identify skewness, modes, and outliers in a histogram.

LO3-4LO3-4 3.2 Frequency Distributions and Histograms3.2 Frequency Distributions and Histograms

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Frequency Polygons and OgivesFrequency Polygons and Ogives

3.3 EXCEL CHARTS3.3 EXCEL CHARTS

This section describes how to use Excel to create charts. Refer to the text.This section describes how to use Excel to create charts. Refer to the text.

3.2 Frequency Distributions and Histograms3.2 Frequency Distributions and Histograms

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• Used to display a time series Used to display a time series or spot trends, or to compare or spot trends, or to compare time periodstime periods..

• Can display several variables Can display several variables at once.at once.

Simple Line ChartsSimple Line Charts

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LO3-5: LO3-5: Make an effective line chart using Excel.Make an effective line chart using Excel.

3.4 Line Charts3.4 Line ChartsLO3-5LO3-5

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Log ScalesLog 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 yourfuture income). It reveals whether the quantity is growing at an

increasing percent (concave upward), constant percent (straight line), or declining percent (concave downward)

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3.4 Line Charts3.4 Line ChartsLO3-5LO3-5

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• Most common way to display attribute data. - Bars represent categories or attributes. - Lengths of bars represent frequencies.

Simple Bar ChartsSimple Bar Charts

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3.5 Bar Charts3.5 Bar Charts

LO3-6: LO3-6: Know the rules for effective bar charts and pie charts.Know the rules for effective bar charts and pie charts.

LO3-6LO3-6

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• Special type of bar chart used in quality management to display the Special type of bar chart used in quality management to display the frequency of defects or errors of different types. frequency of defects or errors of different types.

• Categories are displayed Categories are displayed in in descending descending order order of frequency. of frequency.

• Focus on Focus on significant fewsignificant few (i.e., few (i.e., few categories that categories that account for most defects or errors).account for most defects or errors).

Pareto ChartsPareto Charts

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3.5 Bar Charts3.5 Bar ChartsLO3-6LO3-6

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• A A pie chartpie chart can only convey a general idea of the data. 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 Pie charts should be used to portray data which sum to a total (e.g., percent market

shares).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 ChartAn Oft-Abused Chart

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3.6 Pie Charts3.6 Pie Charts

LO3-6: LO3-6: Know the rules for effective bar charts and pie charts.Know the rules for effective bar charts and pie charts.

LO3-6LO3-6

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• 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.

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3.7 Scatter Plots3.7 Scatter Plots

LO3-7: LO3-7: Make an interpret a scatter plot using Excel.Make an interpret a scatter plot using Excel.

LO3-7LO3-7

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3.8 Tables3.8 Tables

Here are some tips for creating effective 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: LO3-8: Make simple tables and Pivot tables.Make simple tables and Pivot tables.

• TablesTables are the simplest form of data display.

• A compound tablecompound table is a table that contains time series data down the columns and variables across the rows.

LO3-8LO3-8

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3.9 Deceptive Graphs3.9 Deceptive Graphs

LO3-9: LO3-9: Recognize deceptive graphing techniques.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

LO3-9LO3-9