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**Unit 2: Presenting of data**

QUANTITATIVE METHODS FOR BUSINESS Unit 2: Presenting of data

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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

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**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

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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.

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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.

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**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)

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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.

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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

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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

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**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

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**Frequency Distribution**

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

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

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**Histogram Quantitative Methods for Business, Management and Finance**

(3rd Ed) by Louise Swift and Sally Piff

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**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

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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

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**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

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**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

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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

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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

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**Data That Occurs in Pairs**

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

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**Scatter Plot The most effective presentation of Paired Data**

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

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**Time Series Plot When one variable is time**

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

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**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

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**Plot shown to sales representatives**

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

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QUESTIONS ???

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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.

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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?

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