describing data using numerical measures. topics
TRANSCRIPT
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Describing Data Using Numerical Measures
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Topics
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Summary Measures
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Measures of Central Tendency
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Measures of Central Tendency
1 2
1
. .....
nn
n
ii
G x x x
x
1 2
1 1 1...
n
nH
x x x
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Mean (Arithmetic Average)
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Mean (Arithmetic Average)
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Median
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Median
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Median Example
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Mode
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Weighted Mean
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Geometric Mean The geometric mean indicates the central tendency or typical
value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root (where n is the count of numbers) of the product of the numbers.
For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is 2√2 × 8 = 4.
1 21
. .....n
nn i
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The geometric mean only applies to positive numbers in order to avoid taking the root of a negative product
In statistical surveys when proportional differences are more important than the absolute differences, geometric mean referred instead of arithmetic mean.
Geometric Mean
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Harmonic Mean
The harmonic mean H is defined to be the reciprocal of the arithmetic mean of the reciprocals of :
When prices are expressed in quantities (so many units per dollars) harmonic mean should be calculated.
1 2, ,..., nx x x
1 2
1 1 1...
n
nH
x x x
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Shape of a Distribution
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Which Measure of Central Tendency is the “best”?
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Measures of Location (Measures of Statistical Dispersion)
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Percentiles
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Quartiles
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Quartiles
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Box and Whisker Plot
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Constructing the Box and Whisker Plot
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Shape of Box and Whisker Plots
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Distribution Shape and Box and Whisker Plot
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Measures of Statistical Dispersion (Variation)
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Statistical Dispersion (variation)
Measures of statistical dispersion or variation give information on the spread or variability of the data values.
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Range
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Disadvantages of the Range
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Interquartile Range
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Interquartile Range Example
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Variance
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Degrees of Freedom (df)
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Standart Deviation
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Calculation Example: Sample Standart Deviation
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Comparing Standart Deviations
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Coefficient of Variation
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Comparing Coefficients of Variation
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Standardized Data Values
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Standardized Population Values
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Standardized Sample Values
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Standardized Value Example
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Using Probability and Probability Distributions
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Important Terms
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Sample Space
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Events
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Visualizing Events
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Experimental Outcomes
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Probability Concepts
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Probability Concepts
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Independent vs. Dependent Events
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Assigning Probability
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Rules of Probability
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Addition Rule for Elementary Events
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Complement Rule
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Addition Rule for Two Events
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Addition Rule Example
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Addition Rule for Mutually Exclusive Events
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Conditional Probability
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Conditional Probability Example
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Conditional Probability Example
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Conditional Probability Example
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For Independent Events
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Multiplication Rules
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Tree Diagram Example
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Bayes’ Theorem
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Bayes’ Theorem Example
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Bayes’ Theorem Example
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Bayes’ Theorem Example