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Unit 2:Presenting of data

QUANTITATIVE METHODS FOR BUSINESS

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?

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

Population versus SampleA 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

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.

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.

Types of Variables

Data

Qualitative Quantitative

Discrete Continuous

Examples:

Marital Status Political Party Eye Color (Defined categories)

Examples:

Number of Children Defects per hour (Counted items)

Examples:

Weight Voltage (Measured

characteristics)

Summary of Types of Variables

Examples:Classify the following sets of data as

qualitative or quantitative.The religious affiliations of college studentsThe height of each member of a basketball

teamStudents’ scores on the first statistics exam The color of new SUV’s on a car lotThe Olympic track and field world records,

such as the time for the steeplechase.

Examples:Classify the following sets of data as

continuous or discrete.The number of students enrolled in an

accounting classThe number of General Electric microwaves

sold by Home Depot last monthThe acceleration time of an automobileThe temperature of a refrigeratorThe number of people aboard a commercial

airplane

ClassesRepresentations of data often begin

by dividing it into distinct classesThese classes are often of equal widthSet the widths to give somewhere

between 5 and 20 classesBasic pictures are then frequency

distributions, relative frequency distributions and histograms

9Quantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

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

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-0.2

-2.1

1.0 0.1 -0.5

2.4 -2.3

1.5 1.2 -0.6

2.4 -1.2

1.7 -1.3

-1.2

0.9 0.5 0.1 0.1 0.3 -0.4

0.5 0.9

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

Frequency Distribution

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Relative Frequency

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Histogram

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

HistogramsThe area shows the frequencyWith 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

14Quantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

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Stem and Leaf DiagramThe 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 used16

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

Pictures of One Categorical VariableThe 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.

17Quantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

Sample data (survey results)An oil company survey 30 motorists to

find out their preferred location for a new service station.

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Motorist

Location

Motorist

Location

Motorist

Location

1 NW 11 SW 21 NW

2 NE 12 NW 22 SW

3 SE 13 SE 23 SE

4 NW 14 SW 24 SW

5 NW 15 NW 25 NW

6 SW 16 NW 26 SW

7 NE 17 NE 27 SE

8 NE 18 NW 28 SE

9 NW 19 SE 29 NW

10 SW 20 SW 30 NEQuantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

Bar ChartsThe length of bars is proportional to the

number of observations

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Pie ChartsThe angle at the centre is proportional to the

number of observations

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Data That Occurs in Pairs

21Quantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

Scatter PlotThe most effective presentation of Paired

Data

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Time Series PlotWhen one variable is time

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Beware of Misleading PresentationsPoliticians, 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!

24Quantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

25Quantitative Methods for Business, Management and Finance(3rd Ed) by Louise Swift and Sally Piff

Plot shown to sales representatives

Plot shown to shareholders

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QUESTIONS ???

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 FrequencyRelative 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 1.000 due to rounding error.

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?