1. Describing Data Visually
Chapter 3
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

2. Describing Data Visually
Chapter 3
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. Describing Data Visually
Chapter 3
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.

4. 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.

5. 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:

6. 3.1 Stem-and-Leaf Displays and Dot Plots
Chapter 3
Measurement
Look at the data and visualize how they were collected and measured. This data set has high quality data. It is numeric, continuous, and has a ratio scale since there is a meaningful zero.
Sorting (Example: Price/Earnings Ratios)
Sort the data and then summarize in a graphical display. Here are the sorted P/E ratios (random sample of 44 companies; values from Table 3.2).

7. 3.1 Stem-and-leaf Displays and Dot Plots
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.

8. 3.1 Stem-and-Leaf Displays and Dot Plots
Chapter 3
For the 44 P/E ratios, the stem-and-leaf plot is given below.
10’s digit
Unit digit
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. This plot is best used for data that lies within a relatively narrow range.
How many companies in the sample had a P/E ratio of 10?

9. Dot Plots 3.1 Stem-and-Leaf Displays and Dot Plots Chapter 3 LO3-1
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.

10. 3.1 Stem-and-Leaf Displays and Dot Plots
Chapter 3
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.
Discussion: Which
plot is better?

11. 3.1 Stem-and-Leaf Displays and Dot Plots
Chapter 3
Comparing Groups
A stacked dot plot compares two or more groups using a common X-axis scale.
Stem and leaf plots good for small amounts of data.
Dot plots OK for small to medium amounts of data. In class Example: 3.1 (a)

12. 3.2 Frequency Distributions and Histograms
LO3-2
Chapter 3
LO3-2: Create a frequency distribution for a data set
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).

13. 3.2 Frequency Distributions and Histograms
LO3-2
Chapter 3
Constructing a Frequency Distribution
- Herbert Sturges proposed the following rule:
2k-1 = n
How many bins? In other words, what is the value of k here?

14. 3.2 Frequency Distributions and Histograms
LO3-2
Chapter 3
Bin width = (xmax – xmin )/k = (59-7)/6 = 8.67
which is rounded to 10.
In general lower limit is included, and upper limit is excluded for the bin.
However, Excel histograms include upper limit and exclude lower limit.
In class Exercise: 3.4 frequency distribution only.

15. 3.2 Frequency Distributions and Histograms
LO3-2
Chapter 3
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.

16. 3.2 Frequency Distributions and Histograms
LO3-3
Chapter 3
LO3-3: Make a histogram with appropriate bins.
Consider 3 histograms for the P/E ratio data with different bin widths. What do they tell you?

17. 3.2 Frequency Distributions and Histograms
LO3-3
Chapter 3
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
In class Example: 3.4 histogram only.

18. 3.2 Frequency Distributions and Histograms
LO3-3
Chapter 3
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.

19. 3.2 Frequency Distributions and Histograms
LO3-4
Chapter 3
Shape
LO3-4: Identify skewness, modes, and outliers in a histogram.
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.

20. 3.2 Frequency Distributions and Histograms
LO3-4
Chapter 3

21. 3.2 Frequency Distributions and Histograms
Chapter 3
Frequency Polygons and Ogives
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
(we will be seeing in the normal distribution in the next chapter).

22. 3.2 Frequency Distributions and Histograms
Chapter 3
Slope of ogive = percent value of frequency polygon
Frequency Polygons and Ogives

23. 3.3 Excel Charts
Chapter 3
This section describes how to use Excel to create charts. Please refer to the text.

24. 3.4 Line Charts Simple 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.

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.
Should we do the above using two separate line charts instead?

26. 3.4 Line Charts Log Scales Chapter 3 LO3-5
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.

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), US Trade Data set constant percent (straight line), or declining percent (concave downward)

28. Line Chart Rules
Use line charts for time series data, not for cross sectional data.
Time units usually go on the X-axis, increasing from left to right.
Use a zero origin on the Y axis for arithmetic scales
In Class Exercise: 3.13

29. 3.5 Bar Charts Simple Bar Charts Chapter 3 LO3-6
LO3-6: Know the rules for effective bar charts and pie charts.
Simple Bar Charts
Most common way to display attribute data in business. - Bars represent categories or attributes. - Lengths of bars represent frequencies.

30. 3.5 Bar Charts Pareto Charts Chapter 3 LO3-6
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).

31. 3.5 Bar Charts Stacked Column Chart Chapter 3 LO3-6
Column height is the sum of several subtotals. Areas may be compared by color to show patterns in the subgroups and total.
Discuss Vail Example: showing that pricing was important

32. Tips for Bar Charts
Category labels on X axis usually, while numerical levels on Y axis
If a time series is displayed then put years or months or days on X- axis
with increasing time from left to right
Zero origin is usually recommended. This allows each bar length to be
proportional to its value.
Try and put numerical values at the top of each bar or in each bar if stacked.
In Class Exercise: 3.16 (a)

33. 3.6 Pie Charts An Oft-Abused Chart 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). Must represent slices of a whole pie.
A pie chart should only have a few (i.e., 2 to 5) slices.
Each slice can be labeled with data values or percents. 33

34. 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? 34

35. 3.6 Pie Charts Pie Chart Options Chapter 3 LO3-6
Exploded and 3-D pie charts add strong visual impact. But the slice sizes are harder to assess.
In Class Example: 3.19

36. 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. Useful for bivariate data.
Refer to the text for EXCEL outputs.
In class Example: 3.21 36

37. 3.8 Tables Example: School Expenditures Chapter 3
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). 37

38. 3.8 Tables Example: School Expenditures Chapter 3
Units of measure are stated in the footnote.
Note merged headings to group columns.
See text for “Tips for Effective Tables.” Tables”. 38

39. 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. 39

40. 3.9 Deceptive Graphs Chapter 3 LO3-9
LO3-9: Recognize deceptive graphing techniques.
Error 1: Nonzero Origin
A nonzero origin will exaggerate the trend.
Deceptive
Correct 40

41. 3.9 Deceptive Graphs Error 2: Elastic Graph Proportions Chapter 3
LO3-9
Chapter 3
Error 2: Elastic Graph Proportions
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. 41

42. 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. 42

43. 3.9 Deceptive Graphs Error 5: 3-D and Rotated Graphs Chapter 3 LO3-9
Can make trends appear to dwindle into the distance or loom towards you. 43

44. 3.9 Deceptive Graphs Chapter 3 LO3-9 Error 8: Complex Graphs
Avoid if possible. Keep your main objective in mind. Break graph into smaller parts. 44

45. 3.9 Deceptive Graphs Error 11: Area Trick Chapter 3 LO3-9
As figure height increases, so does width, distorting the graph. 45

46. 3.9 Deceptive Graphs Chapter 3 LO3-9
Other deceptive graphing techniques.
Error 3: Dramatic Title and Distracting Pictures
Error 6: Unclear Definitions or Scales
Error 7: Vague Sources
Error 9: Gratuitous Effects
Error 10: Estimated Data 46

47. Homework
3.2 (a) (use stems with values from 8 to 19 for the 10’s place)
3.6
3.12
3.32