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