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GRAPHICAL DESCRIPTIVE STATISTICS FOR QUALITATIVE, TIME SERIES AND 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. - PowerPoint PPT Presentation
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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