Describing Data Using Numerical Measures
Topics
Summary Measures
Measures of Central Tendency
Mean (Arithmetic Average)
Median
Median Example
Mode
Weighted Mean
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.arithmetic meannth rootproduct 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.square root
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
Harmonic Mean The harmonic mean H is defined to be the reciprocal of the arithmetic mean of the reciprocals of :reciprocalarithmetic mean When prices are expressed in quantities (so many units per dollars) harmonic mean should be calculated.
Shape of a Distribution
Which Measure of Central Tendency is the “best”?
Measures of Location (Measures of Statistical Dispersion)
Percentiles
Quartiles
Box and Whisker Plot
Constructing the Box and Whisker Plot
Shape of Box and Whisker Plots
Distribution Shape and Box and Whisker Plot
Measures of Statistical Dispersion (Variation)
Statistical Dispersion (variation) Measures of statistical dispersion or variation give information on the spread or variability of the data values.
Range
Disadvantages of the Range
Interquartile Range
Interquartile Range Example
Variance
Degrees of Freedom (df)
Standart Deviation
Calculation Example: Sample Standart Deviation
Comparing Standart Deviations
Coefficient of Variation
Comparing Coefficients of Variation
Standardized Data Values
Standardized Population Values
Standardized Sample Values
Standardized Value Example
Using Probability and Probability Distributions
Important Terms
Sample Space
Events
Visualizing Events
Experimental Outcomes
Probability Concepts
Independent vs. Dependent Events
Assigning Probability
Rules of Probability
Addition Rule for Elementary Events
Complement Rule
Addition Rule for Two Events
Addition Rule Example
Addition Rule for Mutually Exclusive Events
Conditional Probability
Conditional Probability Example
For Independent Events
Multiplication Rules
Tree Diagram Example
Bayes’ Theorem
Bayes’ Theorem Example