Introduction. Introduction. Course Name: Business Quantitative Analysis QU1. Module: 1 Module Title: Data Description and Presentation. Welcome!

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1 Course Name: Business Quantitative Analysis QU1 Module: 1 Module Title: Data Description and Presentation Lectures and handouts by: Paul Jeyakumar, M.Sc., CGA 1 Welcome! Introduction My presentation focuses on: Key points I consider important in each lesson Areas in which I think you need help 2 Welcome! Introduction My presentation focuses on: Key points I consider important in each lesson Areas in which I think you need help Examination review 3

2 Standard Disclaimers The audio and slides are meant to be used together. Neither is suitable as a stand alone resource. If the lecture inadvertently contradicts the lesson notes, the lesson notes are deemed to be correct. The lecturer does not know the contents of the examination. 4 What do you have to do? Review the Examination Blueprint. Periodically check for updates. 5 What do you have to do? Review the Examination Blueprint. Periodically check for updates. Print the slides. Print the hand-out document. 6

3 What do you have to do? Review the Examination Blueprint. Periodically check for updates. Print the slides. Print the hand-out document. Review the course module. Review the specified readings from the text book. 7 What do you have to do? Review the Examination Blueprint. Periodically check for updates. Print the slides. Print the hand-out document. Review the course module. Review the specified readings from the text book. Keep the above documents handy. Be ready to take notes. 8 Course Purpose Purpose: Necessary background in business statistics and linear programming for the CGA program of professional studies Course coverage: Techniques of data presentation, data collection and data analysis 9

4 Prerequisites Sound understanding of basic mathematics and its application in the business context Basic competence in Excel 10 Course Materials Lesson notes Gerald Kellar and Brian Warrack, Statistics for Management and Economics, Sixth Edition 11 Module 1 Overview Types of data Data presentation 12

5 Introduction to Statistics Learning Objectives Define a population and a sample. Distinguish between descriptive statistics and inferential statistics. Explain the occurrence of sampling error. Describe the benefits of sampling. 13 Population Set of all values under consideration 14 Sample A part (subset) of a population 15

6 Parameters Numerical calculations performed on population data Example: Population mean, µ 16 Statistics Numerical calculations performed on sample data Example: Sample mean 17 Parameters and Samples Arithmetic mean Standard deviation Correlation coefficient Regression coefficient Population µ σ ρ β Sample _ x s r b 18

7 Sampling Error If sample statistics are used to estimate population parameters, there is likely to be an error in the estimate. This error is referred to as a sampling error. 19 Descriptive Statistics Methods of organizing, summarizing, and presenting data Graphical methods Summation techniques 20 Inferential Statistics Drawing conclusions about a population from the analysis of a sample Confidence level Significance level 21

8 Types of Data Learning Objectives Define the terms variable and data. Distinguish between the four types of data. Explain the limitations of ordinal-level data. 22 Variable Characteristics of a population or a sample that is of interest Example: Age of current CGA students 23 Data Actual values of the variable 24

9 Quantitative or Interval Data Real numbers Interval-level and ratio-level Interval-level data: No true zero Example: Temperature Ratio-level data: True zero is a possibility Example: Number of cars in a parking lot 25 Qualitative or Nominal Data Categorical in nature Example: Responses to questions about marital status; single, married, divorced and widowed 26 Ordinal-Level Data Associated with nominal data Ranking Example: Ratings as poor, fair, good, very good and excellent 27

10 Practice Question Are the possible responses nominal, ordinal, interval or ratio? a. Are you a Canadian citizen? b. What is your marital status? c. How many cars are parked outside? d. How much time do you spend on your homework? e. What is your travel time? f. What is your favourite car? 28 Graphing Techniques for Quantitative Data Learning Objectives Describe the use of frequency distribution as a data summary device. Arrange a set of data into classes and calculate frequencies, relative frequencies, and cumulative frequencies. Graph the frequency distribution. 29 Frequency Distribution An arrangement or table that groups data into non-overlapping intervals 30

11 Frequency Distribution Step 1 Number of intervals or classes: Sturges formula: Number of intervals = log (n) where n = the number of observations Example: If n = 60, number of intervals = log (60) = (1.778) = = Number of intervals = 6 (integer only) 31 Frequency Distribution Step 1 (contd.) 2 k n where k = Number of intervals (classes) n = Number of observations With n = 60, 2 6 = 64, and Number of intervals = 6 32 Frequency Distribution Step 2 Determine the class width by subtracting the lowest value from the highest value and dividing the result by the number of intervals. 33

12 Frequency Distribution Step 3 Report each class limits by using the lower limit of the lowest interval and the class width. The class limits are defined so that the classes contain observations up to but not including their upper limits. The classes must be mutually exclusive. Inappropriate classes: 10 x 15 and 15 x Frequency Distribution Step 4 Report the frequency of each class. Determine the relative frequencies for the intervals. If required, determine the cumulative frequencies for the various intervals. 35 Practice Question The number of defective items produced for the last 25 days are as follows: Construct a frequency, relative frequency and cumulative relative frequency distribution for these data. 36

13 Practice Question Solution Step 1: With n = 25, 2 5 = 32, and So the number of intervals = 5 Step 2: With the largest value of 29, and the smallest value of 5, the class width = (29 5)/5 = 5 rounded Step 3: The first class is 5 up to 10, but not including 10. Step 4: No. of observations in class 1 is Solution (continued) Class 5 up to 10 Freq. 6 Rel. Freq Cum. Freq. 6 Cum. Rel. Freq up to up to up to up to Total Histogram The histogram is created by drawing rectangles whose bases are the intervals and whose heights are the frequencies. 39

14 Histogram Exhibit 1:3 40 Shapes of Histogram Symmetric if, when cut in half, the two sides of the histogram have identical shapes. If the long tail extends to the right, it is positively skewed. If the long tail extends to the left, it is negatively skewed. 41 Number of Modal Classes The modal class is the class with the largest number of observations. A frequency distribution with one modal class is referred to as unimodal. A frequency distribution with two modal classes is referred to as bimodal. 42

15 Ogive A graphical representation of the cumulative frequency distribution or the relative cumulative frequency distribution Allows the reader to quickly determine the number, or proportion, of all observations that fall below a certain value 43 Ogive - Example 44 Use of Ogive From the previous Ogive graph: Proportion of observations of age less than 30 = 0.24 Proportion of observations of age more than 40 = = 0.36 Proportion of observations of age between 40 and 50 = =

16 Charts for Nominal-Level Data Learning Objectives Construct pie charts and bar charts for nominal data using Excel. Determine the conditions under which each type of chart should be used. Construct a scatter diagram. 46 Pie Chart Represents nominal-level data A circle with slices of the pie marked off Slices represent categories and their sizes relate to the proportion of all observations 47 Drawing a Pie Chart Dealer C M T U Frequency Rel. Freq

17 Pie Chart 49 Bar Chart Similar to histograms in that the height of the bars represents the frequency, or the relative frequency Spaces between the bars with the same width 50 Bar Chart 51

18 Describing the Relationship Between Two Variables Learning Objectives Construct a scatter diagram showing the relationship between two variables. 52 Scatter Diagram Relationship between two interval variables Independent variables are plotted along the x-axis and the dependent variables are plotted along the y-axis. When the values of the variables tend to vary together, the relationship is positive. If the scatter points are along a straight line, the relationship is linear. 53 Practice Question Income: Dependent variable Education: Independent variable Educ Inc

19 Scatter Diagram 55 Scatter Diagram Interpretation There is a very strong positive relationship between the variables. As years of education increase, there is a tendency for income to linearly increase. 56 Graphical Presentations Analysis There should be a scale. Caption should not influence the reader. Absolute changes can distort information. Stretching the vertical axis can make increases in values appear greater. Stretching horizontal axis can make increases in values appear smaller. Bar chart must have the same bar widths. 57

20 Multiple Choice Question 1 What are you using when data are collected for only a portion of all elements of interest in a statistical study? 1) A sample 2) A population 3) A parameter 4) A frequency distribution Answer: 1 58 Multiple Choice Question 2 You work in an office of 25 people. You ask five of your colleagues about their height. On the basis of this information, you compute the average height of the five colleagues as 170 cm. What is this value an example of? 1) A statistic 2) A sampling error 3) A parameter 4) An observation Answer: 1 59 Multiple Choice Question 3 Which of the following is not the goal of descriptive statistics? 1) Summarizing data 2) Displaying aspects of the collected data 3) Reporting numerical findings 4) Estimating characteristics of a population Answer: 4 60

21 Multiple Choice Question 4 What do you call a summary measure that is computed from a sample to describe a characteristic of a population? 1) A parameter 2) A statistic 3) A population 4) A sampling error Answer: 2 61 Multiple Choice Question 5 What do you call a summary measure that is computed from a population? 1) A parameter 2) A statistic 3) A scatter diagram 4) An ogive Answer: 1 62 Multiple Choice Question 6 Which of the following is correct? 1) The lowest value in a data set must appear in the first class of a grouped frequency distribution. 2) A histogram cannot have more than one mode. 3) Bell-shaped distributions tail off to the right. 4) Ogives are bell-shaped. Answer: 1 63

22 Multiple Choice Question 7 Which of the following is false? 1) A cumulative frequency distribution lists the number of observations that are within or below each of the classes. 2) A frequency distribution with more values to the left and tails to the right is skewed positively. 3) A relative frequency distribution describes the proportion of data values that fall within each class. 4) The class interval in a frequency distribution is the number of data values falling within each class. Answer: 4 64 Multiple Choice Question 8 Which is the most appropriate type of chart for determining the number of observations at or below a specific value? 1) A histogram 2) A pie chart 3) A bar chart 4) An ogive Answer: 4 65 Multiple Choice Question 9 Which is the best type of chart for stressing relative frequencies? 1) A bar chart 2) A pie chart 3) A histogram 4) An ogive Answer: 2 66

23 Multiple Choice Question 10 How can you make the slope of a line graph appear steeper? 1) By stretching the vertical axis 2) By shrinking the horizontal axis 3) By stretching the horizontal axis 4) Both 1) and 2) Answer: 4 67