OPIM 5103 Statistics Looking at Data Computing Summary Statistics

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OPIM 5103 StatisticsLooking at DataComputing
Summary Statistics
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Topic 2 Looking and Examining Data

• Looking at Data (Ch. 2)
• Numerical Data
• Histograms
• Cumulative frequency distributions
• Scatterplots
• Categorical Data
• Bar Charts, Pie Charts, Pareto diagrams
• Contingency Tables Excels PivotTable
• Computing Summary Statistics
• Measures of Central Tendency
• Measures of Dispersion

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Looking at Data

• Example
• House Data

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Types of Data
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Displaying Numerical Data

• Histogram example

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Displaying Numerical Data
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EXCEL Tutorial Histograms

• Heres a PDF document

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Displaying Bivariate Numerical Data

• Scatterplots

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Displaying Categorical Data

• Example bar chart, pie chart, Pareto diagram

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Displaying Categorical Data

• Example bar chart, pie chart, Pareto diagram

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Displaying Categorical Data

• Example bar chart, pie chart, Pareto diagram

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Displaying Bivariate Categorical Data

• Contingency table

Basement
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EXCEL Tutorial PivotTables

• Heres a PDF document

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Computing Summary Statistics from Data

• Central Tendency
• mean
• median
• Spread/Dispersion
• variance
• interquartile range

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Median
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Mean (Arithmetic Mean)

• The most common measure of central tendency
• Affected by extreme values (outliers)

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
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Mean 5
Mean 6
Excel function average(range)
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Median

• Robust measure of central tendency
• Not affected by extreme values
• In an ordered array, the median is the middle
  number

0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12
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Median 5
Median 5
Excel function median(range)
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Quartiles

• Split Ordered Data into 4 Quarters
• Median, A Measure of Central Tendency

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Excel function quartile(range,
number) 0 minimum value 1
Q1 4 maximum value
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Interquartile Range

• Measure of spread/dispersion
• Also known as midspread
• Spread in the middle 50
• Difference between the first and third quartiles
• Not affected by extreme values

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Variance

• Important measure of variation
• Shows variation about the mean
• Sample variance
• Average of squared deviations from the mean
• Standard deviation square root of variance

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Excel functions

• Variance
• VAR(range)
• Standard Deviation
• STDEV(range)

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Comparing Standard Deviations
Data A
Mean 15.5 s 3.338
11 12 13 14 15 16 17 18
19 20 21
Data B
Mean 15.5 s .9258
11 12 13 14 15 16 17 18
19 20 21
Data C
Mean 15.5 s 4.57
11 12 13 14 15 16 17 18
19 20 21
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Coefficient of Correlation

• Measures the strength of the linear relationship
  between two quantitative variables

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Features of Correlation Coefficient

• Unit free
• Ranges between 1 and 1
• The closer to 1, the stronger the negative
  linear relationship
• The closer to 1, the stronger the positive linear
  relationship
• The closer to 0, the weaker any positive linear
  relationship

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Scatter Plots of Data with Various Correlation
Coefficients
Y
Y
Y
X
X
X
r -1
r -.6
r 0
Y
Y
X
X
r 1
r .6