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Describing Data Using Numerical Measures

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Title: Describing Data Using Numerical Measures


1
Describing Data Using Numerical Measures
2
Topics
3
Summary Measures
4
Measures of Central Tendency
5
Measures of Central Tendency
6
Mean (Arithmetic Average)
7
Mean (Arithmetic Average)
8
Median
9
Median
10
Median Example
11
Mode
12
Weighted Mean
13
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.

14
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.

15
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.

16
Shape of a Distribution
17
Which Measure of Central Tendency is the best?
18
Measures of Location (Measures of Statistical
Dispersion)
19
Percentiles
20
Quartiles
21
Quartiles
22
Box and Whisker Plot
23
Constructing the Box and Whisker Plot
24
Shape of Box and Whisker Plots
25
Distribution Shape and Box and Whisker Plot
26
Measures of Statistical Dispersion (Variation)
27
Statistical Dispersion (variation)
  • Measures of statistical dispersion or variation
    give information on the spread or variability of
    the data values.

28
Range
29
Disadvantages of the Range
30
Interquartile Range
31
Interquartile Range Example
32
Variance
33
Degrees of Freedom (df)
34
Standart Deviation
35
Calculation Example Sample Standart Deviation
36
Comparing Standart Deviations
37
Coefficient of Variation
38
Comparing Coefficients of Variation
39
Standardized Data Values
40
Standardized Population Values
41
Standardized Sample Values
42
Standardized Value Example
43
Using Probability and Probability Distributions
44
Important Terms
45
Sample Space
46
Events
47
Visualizing Events
48
Experimental Outcomes
49
Probability Concepts
50
Probability Concepts
51
Independent vs. Dependent Events
52
Assigning Probability
53
Rules of Probability
54
Addition Rule for Elementary Events
55
Complement Rule
56
Addition Rule for Two Events
57
Addition Rule Example
58
Addition Rule for Mutually Exclusive Events
59
Conditional Probability
60
Conditional Probability Example
61
Conditional Probability Example
62
Conditional Probability Example
63
For Independent Events
64
Multiplication Rules
65
Tree Diagram Example
66
Bayes Theorem
67
Bayes Theorem Example
68
Bayes Theorem Example
69
Bayes Theorem Example
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