1. Unit 2: Presenting of data
QUANTITATIVE METHODS FOR BUSINESS
Unit 2:
Presenting of data

2. Objectives
Understand the difference between numerical and categorical data;
Calculate frequencies and relative frequencies;
Construct a histogram of a numerical variable;
Draw a scatter plot of two numerical variables;
Draw a bar chart or pie chart of categorical data;
Be sceptical about published graphs – do they represent the data fairly?
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

3. Population versus Sample
A population is a collection of all possible individuals, objects, or measurements of interest.
A sample is a portion, or part, of the population of interest

4. Types of Variables
Qualitative or Categorical variable - the characteristic being studied is nonnumeric.
EXAMPLES: Gender, type of car owned, country of birth, hair color are examples.
Quantitative or Numerical variable - information is reported numerically.
EXAMPLES: balance in your checking account, minutes remaining in class, or number of students in a class.

5. Types of Variables
Quantitative variables can be classified as either discrete or continuous.
A. Discrete variables: can only assume certain values and there are usually “gaps” between values.
EXAMPLE: the number of bedrooms in a house, or the number of MP3 sold at the Harvey Norman (1,2,3,…,etc).
B. Continuous variable can assume any value within a specified range.
EXAMPLE: The pressure in a tire, the weight of a can, or the height of students in a class.

6. Summary of Types of Variables
Examples:
Marital Status
Political Party
Eye Color
(Defined categories)
Examples:
Number of Children
Defects per hour
(Counted items)
Examples:
Weight
Voltage
(Measured characteristics)

7. Examples:
Classify the following sets of data as qualitative or quantitative.
The religious affiliations of college students
The height of each member of a basketball team
Students’ scores on the first statistics exam
The color of new SUV’s on a car lot
The Olympic track and field world records, such as the time for the steeplechase.

8. Examples:
Classify the following sets of data as continuous or discrete.
The number of students enrolled in an accounting class
The number of General Electric microwaves sold by Home Depot last month
The acceleration time of an automobile
The temperature of a refrigerator
The number of people aboard a commercial airplane

9. Classes
Representations of data often begin by dividing it into distinct classes
These classes are often of equal width
Set the widths to give somewhere between 5 and 20 classes
Basic pictures are then frequency distributions, relative frequency distributions and histograms
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

10. Sample Data (% return on a share)
The following numbers show the percentage return on an ordinary share for 23 months
Data in the current form is not very informative
An analyst might need to describe how the returns are spread or distributed between minimum -2.3 and maximum 2.4.
The distribution can be described in 2 general ways: graphical methods or numerical methods
-0.2
-2.1
1.0
0.1
-0.5
2.4
-2.3
1.5
1.2
-0.6
-1.2
1.7
-1.3
0.9
0.5
0.3
-0.4
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

11. Frequency Distribution
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

12. Relative Frequency
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

13. Histogram Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

14. Histograms The area shows the frequency
With bars of equal widths, this effectively means that the length is proportional to the frequency
The choice of class can change the shape of the diagram
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

16. Stem and Leaf Diagram
The stem and leaf diagram is a quick and useful way of displaying numerical data. It has the advantage, over a histogram, of retaining every value.
To describe the data set of 42, 59, 35, 25, 32
In practice, not widely used
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

17. Pictures of One Categorical Variable
The previous diagrams are good for quantitative values
Sometimes, data are not numerical, but they record an attribute or a quality (e.g. Gender)
Then charts record the number in certain categories.
And we can show it in bar charts or pie charts.
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

18. Sample data (survey results)
An oil company survey 30 motorists to find out their preferred location for a new service station.
Motorist
Location 1 NW 11 SW 21 2 NE 12 22 3 SE 13 23 4 14 24 5 15 25 6 16 26 7 17 27 8 18 28 9 19 29 10 20 30
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

19. Bar Charts
The length of bars is proportional to the number of observations
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

20. Pie Charts
The angle at the centre is proportional to the number of observations
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

21. Data That Occurs in Pairs
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

22. Scatter Plot The most effective presentation of Paired Data
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

23. Time Series Plot When one variable is time
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

24. Beware of Misleading Presentations
Politicians, journalists, advertisers – and other people - are very good at presenting data in a way that is misleading
This is sometimes deliberate as an attempt to support their views
It can also happen accidentally through ignorance
Be careful!
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

25. Plot shown to sales representatives
Plot shown to shareholders
Quantitative Methods for Business, Management and Finance
(3rd Ed) by Louise Swift and Sally Piff

26. QUESTIONS ???

27. Review Question:
The SaveMore Rental Car Agency at the Cincinnati airport would like to examine records from last summer in order to plan for the coming summer demand. The data for last year’s demand, broken down by type of vehicle requested, is shown in the table below.
Vehicle Type
Frequency
Relative Frequency
Sub-compact
545
0.183
Compact
892
0.299
Full-size
740
0.248
Luxury
360
0.121
SUV
280
0.094
Van
168
0.056
Total
2985
1.001*
* Total is not equal to due to rounding error.

28. Review Question:
Construct a frequency and relative frequency bar chart for the data.
Construct a pie chart to display the relative frequency information.
This summer’s demand is expected to be 20% higher than demand for last summer. Approximately how many luxury cars are expected to be rented this summer?