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QM 1 - Intro to Quant Methods. Graphical Descriptive Statistics Charts and Tables Dr. J. Affisco. Organizing Numerical Data. Organizing Numerical Data. Numerical Data. 41, 24, 32, 26, 27, 27, 30, 24, 38, 21. Frequency Distributions Cumulative Distributions. Ordered Array. - PowerPoint PPT Presentation
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QM 1 - Intro to Quant Methods
Graphical Descriptive Statistics
Charts and Tables
Dr. J. Affisco
Organizing Numerical Data
2 144677
3 028
4 1
Organizing Numerical Data
Numerical Data
Ordered Array
Stem and LeafDisplay
Frequency DistributionsCumulative 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
2 1 4 4 6 7 7
Organizing Numerical Data:
•Data in Raw form (as collected):24, 26, 24, 21, 27, 27, 30, 41, 32, 38
•Date Ordered from Smallest to Largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
•Stem and Leaf display:3 0 2 8
4 1
Let’s look at an
Ordered Array and Stem and Leaf
for our Survey Data
using Excel
Ogive
0
20
40
60
80
100
120
10 20 30 40 50 60
0
1
2
3
4
5
6
7
10 20 30 40 50 60
2 144677
3 028
4 1
Organizing Numerical Data
Numerical Data
Ordered Array
Stem and LeafDisplay
Histograms Ogive
Tables
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Frequency DistributionsCumulative Distributions
Polygons
Tabulating Numerical Data:
•Sort Raw Data in Ascending Order: 12, 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
•Compute Class Midpoints: 15, 25, 35, 45, 55
•Count Observations & Assign to Classes
Tabulating Numerical Data: Frequency Distributions
Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
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
Histogram
0
3
65
4
2
001234567
5 15 25 36 45 55 More
Fre
qu
en
cy
Graphing Numerical Data:The Histogram
Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class Midpoints
No Gaps Between
Bars
Graphing Numerical Data:The Frequency Polygon
Frequency
0
1
2
3
4
5
6
7
5 15 25 36 45 55 More
Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class Midpoints
Cumulative CumulativeClass Frequency % Frequency
10 but under 20 3 15
20 but under 30 9 45
30 but under 40 14 70
40 but under 50 18 90
50 but under 60 20 100
Tabulating Numerical Data:Cumulative Frequency
Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Graphing Numerical Data:The Ogive (Cumulative % Polygon)
Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Ogive
0
20
40
60
80
100
120
10 20 30 40 50 60
Class Boundaries
Another Example:
Auto Gas Mileage
Let’s look at a
Frequency Table and a Histogram for
our Survey Data
using Excel
Try This Problem
The Pulse Rate of 10 well-conditioned
athletes is
31,33,36,36,37,38,39,41,44,47
Using four classes create a frequency
table and histogram.
Organizing
Categorical Data
Organizing Categorical Data Univariate Data:
Categorical Data
Tabulating Data
The Summary Table
Graphing Data
Pie Charts
Pareto DiagramBar Charts
Summary Table(for an investor’s portfolio)
Investment Category Amount Percentage (in thousands $)
Stocks 46.5 42.27
Bonds 32 29.09
CD 15.5 14.09
Savings 16 14.55
Total 110 100
Variables are Categorical.
05
1015202530354045
Stocks Bonds Savings CD
0
20
40
60
80
100
120
0 10 20 30 40 50
Stocks
Bonds
Savings
CD
Organizing Categorical Data
Univariate Data: Categorical Data
Tabulating Data
The Summary Table
Graphing Data
Pie Charts
Pareto DiagramBar Charts
Bar Chart(for an investor’s portfolio)
Investor's Porfolio
0 10 20 30 40 50
Stocks
Bonds
CD
Savings
Amount in K$
Pie Chart(for an investor’s portfolio)
Percentages are rounded to the nearest percent.
Amount Invested in K$
Savings
15%
CD 14%
Bonds
29%
Stocks
42%
Pareto Diagram
Pareto diagram
0
10
20
30
40
50
Stocks Bonds Savings CD
0
20
4060
80
100
120
Axis for bar chart shows % invested
in each category.
Axis for line graph shows cumulative % invested.
Organizing Bivariate Categorical Data
•Contingency Tables
•Side by Side Charts
Organizing Categorical Data Bivariate Data:
Contingency Table: 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 49
Savings 16 28 7 51
Total 110 147 67 324
Organizing Categorical Data Bivariate Data:
Comparing Investors
0 10 20 30 40 50 60
Stocks
Bonds
CD
Savings
Investor A Investor B Investor C
Side by SideChart
Let’s look at a
Pie Chart, a Bar Chart, and a Pareto
Diagram for our Survey Data