Describing Data Using Numerical Measures

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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
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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 2v2 8 4.

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Geometric Mean

• 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.

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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.

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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