GRAPHICAL DESCRIPTIVE GRAPHICAL DESCRIPTIVE STATISTICS FOR STATISTICS FOR

QUALITATIVE, TIME SERIES QUALITATIVE, TIME SERIES AND RELATIONAL DATAAND RELATIONAL DATA

Reasons To Collect Data

• Obtain Input to a Research Study

• Measure Performance

• Assist in Formulating Decision Alternatives

• Satisfy Curiosity– Knowledge for the Sake of Knowledge

Random Variables

• Random variables are phenomena or characteristics that are not known in advance

• Data are observations of random variables

TYPES OF DATA

• Qualitative– Result to a survey question is non-numeric

• Categorical Data

• Ordinal (Ranked) Data

• Quantitative– Result to a survey question is a number

• Ratio Data – Has an “absolute 0” point, e.g. age

• Interval – 0 is simply another number – e.g. degrees Fahrenheit

Graphical TechniquesQualitative Data

• Pie Charts

• Bar Charts

Plot of Frequency Distributions

• Objective is to develop a frequency distribution table– Hand Count– Excel Approach

• COUNTIF command

Pie Charts

• Determine the relative frequency for each category

• Apportion sectors (wedges) of a 360 degree circle proportionately

Example

Frequency Distribution of Origin Frequency Distribution of Origin of Car Manufacturerof Car Manufacturer

FrequencyFrequency

AmericanAmerican 1616

AsianAsian 2020

EuropeanEuropean 4 4

Relative FrequencyRelative Frequency

.40.40

.50.50

.10.10

Pie Chart

Bar Charts

• Bars show the frequency or relative frequency of the observations

• Consider the same example

Frequency Bar Chart

Continent

0

5

10

15

20

25

American Asian European

Relative Frequency Bar Chart

EXCELPie Charts

• Example -- 66 people surveyed and asked the color of their car -- Their choices:– Red– Blue– Black– White– Other

• These are recorded in cells A2 to A67 of a spreadsheet

Determining Frequency DistributionsStep 1 – Record Responses in a Column

Record responses Record responses recorded in column Arecorded in column A

Step 2 – Type Categories in another Column

Type Categories in Type Categories in Column BColumn B

Step 3 – Use COUNTIF to Determine Frequencies

=COUNTIF( )=COUNTIF( )

Drag down to C3:C6Drag down to C3:C6

What it should match

(Relative Address)

B2B2

Where data is located

(Drag down)

$A$2:$A$67,$A$2:$A$67,

1.Go to Chart Wizard

2.Select Pie

Creating a Pie Chart

3.Select this sub-type

Click NextClick Next

Creating a Pie Chart - 2

Highlight Cells B1through C6First Column – Labels

Second Column -- Frequencies

Click NextClick Next

Creating a Pie Chart - 3

1.Put in an appropriate title

2.Click Legend Tab

Creating a Pie Chart - 4

1.Uncheck Show legend

2.Click Data Labels Tab

Creating a Pie Chart - 5

Put bullet in Show label and percent

Click FinishClick Finish

Completed Pie Chart

Editing Options

• Enlarge

• Put Labels Inside Wedges

• Change Colors

• Add Text

• Etc.

EXCELBar Charts

• What we call Bar Charts, Excel calls Column Charts– The steps are similar

• If you already have a pie chart, you can convert it to a bar chart as shown on the next slide:

Creating a Bar Chart From a Pie Chart

1. Right Mouse Click on graph

2. Select Chart Type

3. Select Column

Resulting Bar Chart

Line Charts for Time Series Data

• Time series -- Values vs. time– Dow Jones vs. Day– Sales vs. Quarter– Population vs. Year

• Typically depicted as line charts

• In Excel if you already have a bar chart you can convert it to a line chart using the method on the last slide– Otherwise we do the following

Example -- Sales at Epencil.com

1.Go to Chart Wizard

2.Select Line

Click NextClick Next

1.Enter Cells with

With Sales FiguresB2:B8

2.Click Series Tab

1.Enter Chart Title

2.Enter YearsCells A2:A8

Click NextClick Next

Note: In this dialogue box, there are many editing features

2. Entera label for Y-axis

1. Enter a label for X-axis

3.Click Legend Tab

1.Uncheck Show legend

2.

Click FinishClick Finish

Can now edit figure: Resize

Delete Gray BackgroundDelete Lines

Etc.

Scatter Diagrams -- Showing Relationships Between Variables

• A scatter diagram shows the relationship between two quantitative variables as a plot of a series of points (observations) – (Grade vs. Study time)– (Sales vs. Advertising $)– (Production vs. Resources)

• Types of relations that can be detected– Linear (Positive or Negative)

• Least Squares Line -- “Best” line through points– Nonlinear– No Relation

Example

• Sales of Pencils at Epencil vs. Advertising $ spent during the week

1.Click Chart Wizard

2.Select Scatter

Click NextClick Next

1.Enter data columns for both X and Y

with the column for X first.Do not include the labels.

2.Click Series Tab

Enter Chart Title

Click NextClick Next

In this dialogue box there are many editing features

1.Uncheck Show legend2.

Click Titles Tab

1.Enter X-axis Label

2.Enter Y-axis Label

Click FinishClick Finish

Can now edit figure: Resize

Delete Gray BackgroundDelete Lines

Etc.

Determining Trend

• We can have Excel put the best straight line or other curve (parabola, etc.) through these points so that we can easily observe trend

1.Right mouse click on any data point

so that squares appear in the data points

2.Select Add Trendlinefrom the Popup Menu

3.Select Type

(Usually Linear)

Trendline added

How to Lie With Statistics

• Graphs can be used to accurately portray data

• However, sometimes a graph can be distorted in such a way as to skew the information it conveys

• Examples– Fatter or different shaped barsFatter or different shaped bars– Stretched or condensed axesStretched or condensed axes– No indication of a “break” on the axisNo indication of a “break” on the axis– Unlabeled axesUnlabeled axes

Review

• How to construct by hand and by Excel– Pie Charts for Qualitative Data– Bar Charts for Qualitative Data– Line Charts for Time Series Data– Scatter Diagrams to Show Relationships

Between Variables

• How Graphs Can be Deceptive