7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
1/24
Presenting Data in Tables
and Charts
Review of Statistical concepts
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
3/24
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)
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
4/24
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.
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
5/24
Organizing Numerical Data
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
6/24
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:
Organizing Numerical Data
(continued)
2 1 4 4 6 7 7
3 0 2 8
4 1
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
7/24
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
Frequency Distributions
Cumulative Distributions
Polygons
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
8/24
Tabulating Numerical Data:
Frequency Distributions
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
9/24
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
10/24
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
Data in Ordered Array:
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
11/24
Graphing Numerical Data:
The Frequency Polygon
Frequency
0
1
23
4
5
6
7
5 15 25 35 45 55 More
Class Midpoints
Data in Ordered Array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
b l l
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
12/24
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
Data in Ordered Array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
13/24
Graphing Numerical Data:
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
14/24
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
15/24
Tabulating and Graphing
Univariate Categorical Data
Categorical Data
Tabulating Data
The Summary Table
Graphing Data
Pie Charts
Pareto DiagramBar Charts
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
16/24
Summary Table(for an Investors Portfolio)
Investment Category Amount Percentage(in thousands $)
Stocks 46.5 42.27Bonds 32 29.09
CD 15.5 14.09
Savings 16 14.55
Total 110 100
Variables are Categorical
G hi U i i t
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
17/24
Graphing Univariate
Categorical Data
0 10 20 30 40 50
S t ocks
B onds
Savings
CD
Categorical Data
Tabulating Data
The Summary Table
Graphing Data
Pie Charts
Pareto DiagramBar Charts
0
5
10
15
20
25
30
35
40
45
S to ck s B on ds S avin gs C D
0
20
40
60
80
100
120
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
18/24
Bar Chart(for an Investors Portfolio)
Investor's Portfolio
0 10 20 30 40 50
Stocks
Bonds
CD
Savings
Amount in K$
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
19/24
Pie Chart
(for an Investors Portfolio)
Percentages arerounded to the
nearest percent
Amount Invested in K$
Savings
15%
CD
14%
Bonds
29%
Stocks
42%
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
20/24
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
21/24
Tabulating and Graphing
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
22/24
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
23/24
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
7/27/2019 1 A REVIEW OF STATISTICAL CONCEPTS.ppt
24/24
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)