1 A REVIEW OF STATISTICAL CONCEPTS.ppt

7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt

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Presenting Data in Tables

and Charts

Review of Statistical concepts


2/24

Topics

Random variable

Organizing Numerical Data

The Ordered Array and Stem-Leaf Display

Tabulating and Graphing Univariate Numerical Data

Frequency Distributions: Tables, Histograms, Polygons

Cumulative Distributions: Tables, the Ogive

Graphing Bivariate Numerical Data


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Topics

Tabulating and Graphing Univariate

Categorical Data

The Summary Table

Bar and Pie Charts, the Pareto Diagram

Tabulating and Graphing Bivariate Categorical

Data

Contingency Tables Side by Side Bar Charts

Graphical Excellence and Common Errors in

Presenting Data

(continued)


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Random Variable

Random Variable isone that varies as amatter of chance and

it follows some sortof probabilitydistribution

eg. Dimension of a

component Distribution may be

continuous or discreet

continuous discreet

The variable cantake any value in its

range of variationeg. Dimension,weight, resistance,tensile strength

The variable cantake only specific

values in its rangeof variation eg. No.of defectives in asample, no. ofdefects in an item,no. of vehicles goingthrough a crossing

Normal, uniform,erlang, triangular,

weibull distributions

Hypergeometric,binomial, Poisson,

geometric, negativebinomial etc.


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2 144677

3 028

4 1

Numerical Data

Ordered Array

Stemand Leaf

Display

Frequency Distributions

Cumulative Distributions

Histograms

Polygons

Ogive

Tables

41, 24, 32, 26, 27, 27, 30, 24, 38, 21

21, 24, 24, 26, 27, 27, 30, 32, 38, 41


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Data in RawForm (as Collected):24, 26, 24, 21, 27, 27, 30, 41, 32, 38

Data inOrdered Arrayfrom Smallest to Largest:21, 24, 24, 26, 27, 27, 30, 32, 38, 41

Stem-and-Leaf Display:


(continued)

2 1 4 4 6 7 7

3 0 2 8

4 1


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Tabulating and Graphing

Numerical Data

Ogive

0

20

40

60

80

10 0

12 0

1 0 2 0 3 0 4 0 5 0 6 0

0

1

2

3

4

5

6

7

1 0 2 0 3 0 4 0 5 0 6 0

2 144677

3 028

4 1

Numerical Data

Ordered Array

StemandLeaf

Display

Histograms Ogive

Tables

41, 24, 32, 26, 27, 27, 30, 24, 38, 21

21, 24, 24, 26, 27, 27, 30, 32, 38, 41


Cumulative Distributions

Polygons


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Tabulating Numerical Data:


Sort Raw Data in Ascending Order12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find Range: 58 - 12 = 46

Select Number of Classes: 5(usually between 5 and 15) Compute Class Interval (Width): 10 (46/5 then round up)

Determine Class Boundaries (Limits):10, 20, 30, 40, 50, 60 Compute Class Midpoints: 15, 25, 35, 45, 55

Count Observations & Assign to Classes


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Frequency Distributions, Relative Frequency

Distributions and Percentage Distributions

Class Frequency

10 but under 20 3 .15 15

20 but under 30 6 .30 30

30 but under 40 5 .25 25

40 but under 50 4 .20 20

50 but under 60 2 .10 10

Total 20 1 100

RelativeFrequency

Percentage

Data in Ordered Array:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58


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Graphing Numerical Data:

The Histogram

Histogram

0

3

6

5

4

2

00

1

2

3

4

5

6

7

5 15 25 35 45 55 More

Fre

quency


12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

No Gaps

Between

Bars

Class MidpointsClass Boundaries


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The Frequency Polygon

Frequency

0

1

23

4

5

6

7

5 15 25 35 45 55 More

Class Midpoints


12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

b l l


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Tabulating Numerical Data:

Cumulative Frequency

Lower Cumulative CumulativeLimit Frequency % Frequency

10 0 0

20 3 15

30 9 4540 14 70

50 18 90

60 20 100


12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58


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The Ogive (Cumulative % Polygon)

Ogive

0

20

40

60

80

100

10 20 30 40 50 60

Class Boundaries (Not M idpoints)

Data in Ordered Array :

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58


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Graphing Bivariate NumericalData (Scatter Plot)

Mutual Funds Scatter Plot

0

10

20

30

40

0 10 20 30 40

Net Asset Values

TotalYear

to

D

ateReturn

(%)

T b l ti d G hi


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Univariate Categorical Data

Categorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts


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Summary Table(for an Investors Portfolio)

Investment Category Amount Percentage(in thousands $)

Stocks 46.5 42.27Bonds 32 29.09

CD 15.5 14.09

Savings 16 14.55

Total 110 100

Variables are Categorical

G hi U i i t


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Graphing Univariate

Categorical Data

0 10 20 30 40 50

S t ocks

B onds

Savings

CD

Categorical Data

Tabulating Data

The Summary Table

Graphing Data

Pie Charts

Pareto DiagramBar Charts

0

5

10

15

20

25

30

35

40

45

S to ck s B on ds S avin gs C D

0

20

40

60

80

100

120


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Bar Chart(for an Investors Portfolio)

Investor's Portfolio

0 10 20 30 40 50

Stocks

Bonds

CD

Savings

Amount in K$


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Pie Chart

(for an Investors Portfolio)

Percentages arerounded to the

nearest percent

Amount Invested in K$

Savings

15%

CD

14%

Bonds

29%

Stocks

42%


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Pareto Diagram

Axis for linegraph

shows

cumulative

% invested

Axis for

bar

chart

shows

%

invested

in each

category

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Stocks Bonds Savings CD

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

T b l ti d G hi


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Bivariate Categorical Data

Contingency Tables: Investment in Thousands of Dollars

Investment Investor A Investor B Investor C Total

Category

Stocks 46.5 55 27.5 129

Bonds 32 44 19 95

CD 15.5 20 13.5 49Savings 16 28 7 51

Total 110 147 67 324


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Tabulating and GraphingBivariate Categorical Data

Side by Side Charts

Comparing Investors

0 10 20 30 40 50 60

Stocks

Bonds

CD

Savings

Investor A Investor B Investor C


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Principles of Graphical Excellence

Well-Designed Presentation of Data thatProvides: Substance

Statistics Design

Communicate Complex Ideas with Clarity,Precision and Efficiency

Gives the Largest Number of Ideas in theMost Efficient Manner

Almost Always Involves Several Dimensions

Telling the Truth about the Data


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Summary

Tabulated and Graphed Univariate CategoricalData

The Summary Table

Bar and Pie Charts, the Pareto Diagram

Tabulated and Graphed Bivariate CategoricalData

Contingency Tables

Side by Side Charts

Discussed Graphical Excellence

(continued)

Documents

1 A REVIEW OF STATISTICAL CONCEPTS.ppt