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

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Presentation on theme: "1 Unit 2: Presenting of data QUANTITATIVE METHODS FOR BUSINESS."— Presentation transcript:

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

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? 2 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 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

6 Data QualitativeQuantitative DiscreteContinuous 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

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

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

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

13 Histogram 13 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 14 Quantitative Methods for Business, Management and Finance (3rd Ed) by Louise Swift and Sally Piff

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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 16 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. 17 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. 18 MotoristLocationMotoristLocationMotoristLocation 1NW11SW21NW 2NE12NW22SW 3SE13SE23SE 4NW14SW24SW 5NW15NW25NW 6SW16NW26SW 7NE17NE27SE 8NE18NW28SE 9NW19SE29NW 10SW20SW30NE 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 19 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 20 Quantitative Methods for Business, Management and Finance (3rd Ed) by Louise Swift and Sally Piff

21 Data That Occurs in Pairs 21 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 22 Quantitative Methods for Business, Management and Finance (3rd Ed) by Louise Swift and Sally Piff

23 Time Series Plot When one variable is time 23 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! 24 Quantitative Methods for Business, Management and Finance (3rd Ed) by Louise Swift and Sally Piff

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

26 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 TypeFrequency Relative Frequency Sub-compact Compact Full-size Luxury SUV Van Total * * 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?


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