Prepared by Lloyd R. Jaisingh

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A PowerPoint Presentation Package to Accompany. Applied Statistics in Business &amp; Economics, 4 th edition David P. Doane and Lori E. Seward. Prepared by Lloyd R. Jaisingh. Chapter Contents 3.1 Stem-and-Leaf Displays and Dot Plots 3.2 Frequency Distributions and Histograms

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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

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

Describing Data Visually

Chapter 3

Chapter Learning Objectives

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

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

LO3-3Make a histogram with appropriate bins.

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

LO3-5Make an effective line chart using Excel.

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

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

LO3-8Make simple tables and pivot tables.

LO3-9Recognize deceptive graphing techniques.

Describing Data Visually

Chapter 3

3.1 Stem-and-leaf Displays and Dot Plots

Chapter 3

• 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.

3.1 Stem-and-leaf Displays and Dot Plots

Chapter 3

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

3.1 Stem-and-leaf Displays and Dot Plots

Chapter 3

• Measurement
• Look at the data and visualize how it was 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).

3.1 Stem-and-leaf Displays and Dot Plots

LO3-1

Chapter 3

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 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.

3.1 Stem-and-leaf Displays and Dot Plots

LO3-1

Chapter 3

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.

3.1 Stem-and-leaf Displays and Dot Plots

LO3-1

Chapter 3

• 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.

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

• 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).
• 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 piled up vertically.

3.1 Stem-and-leaf Displays and Dot Plots

LO3-1

Chapter 3

• Range of data shows dispersion.
• Clustering shows central tendency.

3.2 Frequency Distributions and Histograms

LO3-2

Chapter 3

Bins and Bin Limits

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

• A frequency distributionis a table formed by classifying n data values into k classes (bins).
• Bin limitsdefine the values to be included in each bin. Widths must all be the same.
• Frequencies are the number of observations within each bin.
• Expressas relative frequencies(frequency divided by the total) or percentages (relative frequency times 100).

3.2 Frequency Distributions and Histograms

LO3-3

Chapter 3

LO3-3: Make a histogram with appropriate bins.

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.

One can use appropriate technology to construct histograms

3.2 Frequency Distributions and Histograms

LO3-4

Chapter 3

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

3.2 Frequency Distributions and Histograms

Chapter 3

Frequency Polygons and Ogives

3.3 EXCEL CHARTS

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

3.4 Line Charts

LO3-5

Chapter 3

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.

3.4 Line Charts

LO3-5

Chapter 3

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)

3.5 Bar Charts

LO3-6

Chapter 3

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

Simple Bar Charts

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

3.5 Bar Charts

LO3-6

Chapter 3

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).

3.6 Pie Charts

LO3-6

Chapter 3

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 should be labeled with data values or percents.

3.7 Scatter Plots

LO3-7

Chapter 3

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

• Scatter plots can convey patterns in data pairs that would not be apparent from a table.

3.8 Tables

LO3-8

Chapter 3

LO3-8: Make simple tables and Pivot tables.

• Tablesare the simplest form of data display.
• A compound tableis a table that contains time series data down the columns and variables across the rows.

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.

3.9 Deceptive Graphs

LO3-9

Chapter 3

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