Download Chap. 1: Introduction

Statistical Methods
© 1997 Prentice-Hall, Inc.
Statistical
Statistical
Methods
Methods
Descriptive
Descriptive
Statistics
Statistics
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Inferential
Inferential
Statistics
Statistics
Descriptive Statistics
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Involves
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Collecting data
Presenting data
Characterizing
data
Purpose
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Describe data
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Inferential Statistics
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Involves
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Estimation
Hypothesis
testing
Purpose
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Make decisions
about population
characteristics
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Population?
Key Terms
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Population (universe)
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Sample
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Portion of population
Parameter
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All items of interest
Summary measure about population
Statistic
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Summary measure about sample
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Data Types
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Data
Data
Numerical
Numerical
(Quantitative)
(Quantitative)
Discrete
Discrete
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Continuous
Continuous
Categorical
Categorical
(Qualitative)
(Qualitative)
Data Type Examples
© 1997 Prentice-Hall, Inc.
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Numerical
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Discrete
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Continuous
s
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To how many magazines do you subscribe
currently? ___ (Number)
How tall are you? ___ (Inches)
Categorical
s
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Do you own savings bonds? __ Yes __ No
How Are Data Measured?
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Nominal scale
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Ordinal scale
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Interval scale
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Ratio scale
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Standard Notation
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Measure
Mean
Stand. Dev.
Sample
Population
X

S

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Variance
S
22
Size
n
N
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Numerical Data Properties
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Central Tendency
(Location)
Variation
(Dispersion)
Shape
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Numerical Data
Properties & Measures
Numerical
Numerical Data
Data
Properties
Properties
Central
Central
Tendency
Tendency
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Variation
Variation
Shape
Shape
Mean
Mean
Range
Range
Skew
Skew
Median
Median
Kurtosis
Kurtosis
Mode
Mode
Interquartile
Interquartile
Range
Range
Variance
Variance
Midrange
Midrange
Standard
Standard Deviation
Deviation
Midhinge
Midhinge
Coeff.
Coeff. of
of Variation
Variation
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Central Tendency
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Mean
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Measure of central tendency
Most common measure
Acts as ‘balance point’
Affected by extreme values (‘outliers’)
Formula (sample mean):
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X 
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 Xi
i 1
n
X1  X 2    X n

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Median
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Measure of central tendency
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Middle value in ordered sequence
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If odd n, middle value of sequence
If even n, average of 2 middle values
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Not affected by extreme values
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Position of median in sequence
n1
Positioning Point 
2
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Mode
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Measure of central tendency
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Value that occurs most often
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Not affected by extreme values
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May be no mode or several modes
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May be used for numerical &
categorical data
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Quartiles
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Measure of noncentral tendency
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Split ordered data into 4 quarters
25%
25%
Q1
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25%
Q2
25%
Q3
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Summary of
Central Tendency
Measure
Equation
Measure
Equation
Mean
X
Mean
Xii // nn
Median
(n+1)
Median
(n+1) Position
Position
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Mode
none
Mode
none
 X argest
Midrange
Xsmallest
Midrange X
smallest  Xll arg
est
22
Midhinge
Q
Midhinge
Q11  Q
Q33
22
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Description
Description
Balance
Balance point
point
Middle
Middle value
value when
when
ordered
ordered
Most
Most frequent
frequent
Middle
Middle of
of smallest
smallest
&
& largest
largest
Middle
Middle of
of 1st
1st &
&
3rd
3rd quartile
quartile where
where
Q
Qii == ii (n+1)/4
(n+1)/4
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Variation
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Range
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Measure of dispersion
n
Difference between largest &
smallest observations
Range  X l arg est  X smallest
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Ignores how data are distributed
77 88 99 10
10
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77 88 99 10
10
Interquartile Range
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Measure of dispersion
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Also called midspread
n
Spread in middle 50%
n
Not affected by extreme values
n
Formula:
Interquartile Range  Q 3  Q1
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© 1997 Prentice-Hall, Inc.
Variance &
Standard Deviation
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Measures of dispersion
n
Most common measures
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Consider how data are distributed
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Show variation about mean (X or )
XX == 8.3
8.3
44 66
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88 10
10 12
12
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DISPERSION ABOUT
THE MEAN
•Variance
s2=
  X - X
n -1
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2
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DISPERSION ABOUT
MEAN (cont.)
•Standard deviation (sd)
s=
  X - X
n -1
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2
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PROPERTIES OF THE
STANDARD DEVIATION IN
A NORMAL CURVE
X
1s
68%
X
2s
95%
X
3s
99%
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Summary of
Variation Measures
Measure
Measure
Range
Range
Equation
Description
Equation
Description
X
Xlargest
Xsmallest
Total spread
spread
largest -- X
smallest Total
Interquartile
Interquartile range
range
Standard
Standard deviation
deviation
(Sample)
(Sample)
 XXii  XX2
Spread
Spread of
of middle
middle 50%
50%
Dispersion
Dispersion about
about
sample
sample mean
mean
Standard
Standard deviation
deviation
(Population)
(Population)
 XXii  2
Dispersion
Dispersion about
about
population
population mean
mean
Variance
Variance
(Sample)
(Sample)
Coeff.
Coeff. of
of variation
variation
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Q
Q33 -- Q
Q11
2
nn  11
2
N
N
2
(X
(Xii -X)
-X)2
nn -- 11
(S
(S /X)100%
/X)100%
Squared
Squared dispersion
dispersion
about
about sample
sample mean
mean
Relative
Relative variation
variation
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Shape
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Shape
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Describes how data are distributed
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Measures of shape
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Skew: Symmetry
Left-Skewed
Mean Median Mode
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Symmetric
Mean = Median = Mode
Right-Skewed
Mode Median Mean
Box-and-Whisker Plot
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Graphical display of data using
5-number summary
Xsmallest
Q
Median
Q
1
33
smallest
1
4
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6
8
10
Xlargest
largest
12
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Shape &
Box-and-Whisker Plot
Left-Skewed
Q1 Median Q3
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Symmetric
Q1
Median Q3
Right-Skewed
Q1 Median Q3
Conclusion
© 1997 Prentice-Hall, Inc.
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Explained numerical data properties
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Described summary measures
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Central tendency
Variation
Shape
Analyzed numerical data using
summary measures
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This Class...
© 1997 Prentice-Hall, Inc.
Please take a moment to answer the
following questions in writing:
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What was the most important thing
you learned in class today?
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What do you still have questions
about?
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How can today’s class be improved?
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