GRAPHICAL DESCRIPTIVE STATISTICS FOR QUANTITATIVE DATA

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• GRAPHICAL DESCRIPTIVE STATISTICS FOR QUANTITATIVE
  DATA

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Graphical TechniquesQuantitative 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
• Excel in the lower interval
• Inclusion of Outliers? unrepresentative data
  far above or far below most of the rest of the
  data
• Seek reason for outliers
• Relative Frequency (Percentage) Histograms
• Cumulative 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
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RELATIVE FREQUENCY HISTOGRAM
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 Isnt There?
• Go to Tools Menu
• Select Add-Ins

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EXCELHistograms

• Basic Approach
• Put Data in a Column
• Create Bins (Measurement Classes)
• Go To Tools
• Select Data Analysis
• Select Histogram
• Check Chart Output

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(No Transcript)
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CREATE BINS
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TOOLS/DATA ANALYSIS/HISTOGRAM
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Histogram Dialogue Box
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Resizing
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Result of Resizing
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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

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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
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Creating Relative Frequencies
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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
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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 lt
27,500)
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EXCEL Ogives
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(No Transcript)
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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