graphical descriptive statistics for quantitative data
DESCRIPTION
GRAPHICAL DESCRIPTIVE STATISTICS FOR QUANTITATIVE DATA. Graphical Techniques Quantitative Data. Histograms Consider Boundaries of measurement classes Choose values that are easy to read/understand Number of classes will “fall out” Where to place data occurring at “break points” - PowerPoint PPT PresentationTRANSCRIPT
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GRAPHICAL DESCRIPTIVE GRAPHICAL DESCRIPTIVE STATISTICS FOR STATISTICS FOR
QUANTITATIVE DATAQUANTITATIVE DATA
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Graphical TechniquesQuantitative Data
• HistogramsHistograms– Consider
• Boundaries of measurement classesmeasurement classes– Choose values that are easy to read/understand– Number of classes will “fall out”
• Where to place data occurring at “break points”“break points”– Excel Excel – in the lower interval
• Inclusion of Outliers?Outliers? – unrepresentative data far above or far below most of the rest of the data
– Seek reason for outliers
• Relative Frequency (Percentage) HistogramsRelative Frequency (Percentage) Histograms• Cumulative Relative Frequency OgivesCumulative Relative Frequency Ogives
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Frequency Distributions
• Take a Survey of Incomes of 200 High School Graduates 2 Years After Graduation
• Results: $31,500, $26,900, …., $26,100• Create Class Intervals So Data Can Convey
Information– Not too many– Not too few– Include All Data (?) --- Outliers– Intervals of Equal Size
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Results
Income Frequency Rel. Freq.
$15,000-$20,000 9 9/200 = .045
$20,000-$25,000 34 34/200 = .170
$25,000-$30,000 91 91/200 = .455
$30,000-$35,000 61 61/200 = .305
$35,000-$40,000 5 5/200 = .025
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Histogram
Incomes
0
20
40
60
80
100
17500 22500 27500 32500 37500
INCOME
Fre
qu
en
cy
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RELATIVE FREQUENCY HISTOGRAM
Incomes
0
0.1
0.2
0.3
0.4
0.5
17500 22500 27500 32500 37500
INCOME
Re
lati
ve
Fre
qu
en
cy
Same shape as histogram – different scale on y-axis
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EXCELDATA ANALYSIS
• Go to Tools Menu – Select Data Analysis
• What If Data Analysis Isn’t There?– Go to Tools Menu
• Select Add-Ins
Check Analysis Tool Pak
Check Analysis Tool Pak-VBA
Click OK
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EXCELHistograms
• Basic Approach:– Put Data in a Column– Create Bins (Measurement Classes)– Go To ToolsTools
Select Data Analysis Data Analysis
Select Histogram Histogram
Check Chart OutputChart Output
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Data put into a column
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CREATE BINS
2.First entry should be less than lowest
value – actually the lower bound of the lower bound of the first measurement classfirst measurement class – this allows us to begin the histogram at a value >0.
3.Enter the upper bound of upper bound of
the first measurement classthe first measurement class
4.Highlight the first two
entries and drag down to the upper bound of the last
measurement class
++
1.
Enter label for X-Axis
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TOOLS/DATA ANALYSIS/HISTOGRAM
Go to ToolsSelect Data Analysis
Select Histogram
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Histogram Dialogue Box
1. Enter cells containing data including label
2. Entercells containing bins including label
3. CheckLabels
5. Enterwhere you want the output
4. CheckChart Output
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Resizing
Grab Lower Corner and
drag to resize
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Result of Resizing
Click and Delete
Click and Rename
Click in Grey Area and Delete
Change Numbers to Midpoint ValuesDelete first entry (15000)
and last entry (More)
To close gap width:Right mouse click on a barSelect Format Data SeriesFormat Data Series
Select OptionsOptionsSet Gap WidthGap Width = 0
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Resulting Histogram
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Relative Frequency
• Proportion of Data in a Particular Class
• Divide Frequencies by 200 gives these results:
Income Frequency Relative Frequency $15,000-$20,000 9 .045 $20,000-$25,000 34 .170 $25,000-$30,000 91 .455 $30,000-$35,000 61 .305 $35,000-$40,000 5 .025 200 1.000
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Relative Frequency Histogram
• Change the numbers on the y-axis to percentages
• Can manipulate Excel Histogram– Numbers on Y-axis appear in column B– Somewhere create a cell with the formula =B2/200
(Say in cell B12)– Drag down until all relative frequencies are shown– Highlight this new set of numbers and press COPY– Then PASTE SPECIAL (Values) these numbers
back into cell B2– Erase numbers in cells B12 and below– Change Name in cell B1 and on Y-Axis to Relative
Frequency
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Creating Relative Frequencies
3. Put cursor in cell B2
1. Enter =B2/200
Drag to B18
Then highlight B12:B18
2. Select Copy
4. Go to Edit
Select Paste Special
5. Select Values
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Creating Relative Frequencies
6. Change to Relative Frequency
7. Highlight and delete
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Cumulative Relative Frequencies
• Give the proportion of values that are less than the upper boundary point of the class
• Cumulative frequency for first class is the relative frequency
• For subsequent classes cumulative frequency = relative frequency + cumulative frequency of previous class
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Cumulative Relative Frequencies
Income Frequency Relative Frequency Cumulative $15,000-$20,000 9 .045 .045 $20,000-$25,000 34 .170 .215 $25,000-$30,000 91 .455 .670 $30,000-$35,000 61 .305 .975 $35,000-$40,000 5 .025 1.000 200 1.000
The same as the
relative frequency.670 =
.455 + .215
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Ogives
• Line graph of cumulative relative frequencies– Begin with y-value = 0 at $15,000 and draw line
to .045 at $20,000– Draw line from .045 at $20,000 to .215 at $25,000– Draw line from .215 at $25,000 to .670 at $30,000– Draw line from .670 at $30,000 to .975 at $35,000– Draw line from .975 at $35,000 to 1 at $40,000– Draw line flat at 1 (to infinity)
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Result
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Using Ogives to Approximate Prob (Income < $27,500)
27500
0.44
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EXCEL Ogives
Check both
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2.
Delete Legend
4.
Change Names
1.
Resize
6.
Delete More
3.
Delete Background
5.
Right Mouse Click
On any bar --Delete
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RESULT
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Review
• Frequency Distributions
• Frequency Histograms
• Relative Frequency Distributions
• Relative Frequency Histograms
• Cumulative Relative Frequencies
• Cumulative Relative Frequency Ogives