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QMS 102 (49)
Chapter 2

QMS102-Business Statistics I Chapter 2 and 3

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Department
Quantitative Methods
Course
QMS 102
Professor
Jason Chin- Tiong Chan
Semester
Fall

Description
QMS102-Business Statistics I Chapter 2 and 3 Chapter 2 and 3 Organize Qualitative and Quantitative Data Graphically Today’s Outcomes 1. Review-Chapter1 and Chapter3.1 2. Create tables, bar graphs, pie charts and line graphs for qualitative (categorical) data 3. Create frequency distributions, and graphical charts (histogram and ogive) for quantitative (numerical) data Variables 1. A characteristic or quantity that can vary 2. Example: Gender, age, cleanliness rating, staff friendliness rating, and purchase amount. Qualitative(Categorical) and Quantitative(Numerical) data Qualitative data 1. Data containing descriptive information in words or numbers (numbers represent codes for associated words) 2. Example: Gender, staff friendliness rating, customer satisfaction Quantitative data 1. Data containing numerical information. 2. Example: Age, purchase amount Quantitative Data: Discrete and Continuous data Discrete data 1. Data that can take only certain values within a given range. 2. Example: number of customers Continuous data 1. Data that can take on infinite possible values within a given range 2. Example: purchase amount Example1 Part I: Classify the following sets of data as categorical or numerical ___________ a. The amount of investment in Tax-Free Savings Account (TFSA) ___________ b. The client’s gender Fall2012 Page #1 QMS102-Business Statistics I Chapter 2 and 3 ___________ c. The interest rate (in percent) __________ d. Employee’s performance __________ e. The number of customers in the Ryerson Bank. Part II: Classify the following sets of data as continuous or discrete ____________ f. The number of clients who have TFSA with Ryerson Bank ____________ g. The average yearly salary for a Certified General Accountant ____________ h. The month(s) in which a firm’s employees choose to take their vacations. ____________ i. The daily closing price of the Ryerson.COM stock. Tables, Bar Charts and Pie Charts for Qualitative(Categorical) Data Tables Consists of one variable Cross-classification Table/ Crosstabs / Contingency Tables Consists of two variables Bar Charts Bar Chart shows each category, the length of each represent the amount, frequency or percentage of values falling into a category. Pie Charts 1. A circle divided into sectors whose areas are proportional to the quantities represented. 2. It shows relative comparison- in term of percentage. (It is the best way of comparing individual categories to the total) 3. The following information has to be included in pie chart: title, legend and count/%. Fall2012 Page #2 QMS102-Business Statistics I Chapter 2 and 3 Example1: The following data show the mode of transportation that 30 people used to commute to work during the last summer. These 30 people live and work in the GTA. No. Gender Age Mode of No. Gender Age Mode of Group Transportation Group Transportation to work to work 1 Male 16-25 Bicycle 16 Female 16-25 Bicycle 2 Female 36-45 Walking 17 Female 26-35 TTC 3 Male 46-55 TTC 18 Female 16-25 Bicycle 4 Male 46-55 Car 19 Female 16-25 TTC 5 Female 36-45 Other Method 20 Female 16-25 Walking 6 Female 26-35 Walking 21 Male 36-55 Bicycle 7 Male 26-35 Bicycle 22 Female 16-25 Other Method 8 Female 56-65 TTC 23 Male 56-65 Walking 9 Male 56-65 TTC 24 Female 36-45 Bicycle 10 Male 16-25 Bicycle 25 Male 56-65 Car 11 Male 46-55 TTC 26 Male 46-55 Car 12 Female 46-55 TTC 27 Male 46-55 Bicycle 13 Female 46-55 TTC 28 Male 56-65 Other Method 14 Male 26-35 Bicycle 29 Female 16-25 TTC 15 Male 26-35 Bicycle 30 Female 16-25 Bicycle Construct the following: a. a table, b. a simple bar chart, and c. a pie chart to show the mode of transportation that the 30 people listed above used to commute to work during the last summer. These 30 people live and work in the GTA. a. The table shows the mode of transportation that 30 people used to commute to work during the last summer. These 30 people live and work in the GTA. Mode of Transportation To Work Number of Respondents Bicycle 11 Car 3 TTC 9 Walking 4 Other Method 3 b. The simple bar Chart shows the mode of transportation that 30 people used to commute to work during the last summer. These 30 people live and work in the GTA. Fall2012 Page #3 QMS102-Business Statistics I Chapter 2 and 3 c. Mode of transportation Number of respondents Percent to Work Bicycle 11 36.7% Car 3 10.0% TTC 9 30.0% Walking 4 13.3% Other Method 3 10.0% The Pie Chart shows the mode of transportation that 30 people used to commute to work in last summer. These 30 people live and work in the GTA Fall2012 Page #4 QMS102-Business Statistics I Chapter 2 and 3 10.0% 13.3% 36.7% Bicycle Car TTC Walking Other Method 30.0% 10.0% Construct a contingency table and a clustered graph show that the mode of transportation that the 30 people under study used to commute to work in last summer and their gender Title: The contingency table shows the mode of transportation that 30 people used to commute to work during the last summer and their gender Mode of Gender Transportation Female Male Bicycle Car TTC Walking Other Method Title: The clustered bar chart shows the mode of transportation that 30 people used to commute to work during the last summer and their gender Fall2012 Page #5 QMS102-Business Statistics I Chapter 2 and 3 Example2 The following data represent the average values of the U.S. dollars in Canadian cents for the period 1992 to 2003, reported on a yearly basis by the Bank of Canada. Years 1992 1993 1994 1995 1996 1997 U.S.dollars (in Cdn. Cents) 120.8 127.0 136.6 137.2 136.3 138.4 Years 1998 1999 2000 2001 2002 2003 U.S.dollars (in Cdn. Cents) 148.3 148.5 148.5 154.9 157.0 158.0 Construct a single graph to present the above data. The line graph shows the 120 mutual funds that are classified according to the risk level of mutual funds. Fall2012 Page #6 QMS102-Business Statistics I Chapter 2 and 3 160 155 s 150 n e 145 C a 140 d 135 a a 130 C ( 125 a l 120 d S 115 U 110 105 100 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Year Quantitative (Numerical) Data can be organized into a. Stem-and-Leaf Fall2012 Page #7 QMS102-Business Statistics I Chapter 2 and 3 b. Array c. Frequency, Relative Frequency, Cumulative Frequency Distribution d. Histogram e. Polygon f. Ogive (Cumulative Frequency Diagram) a. Stem-and-Leaf 1. Each numerical value divides into two parts. The leading digit(s) becomes the stem and the trailing digit the leaf. The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis. b. Array 1. Arrange the data in ascending or descending order 2. Advantages a. Identify the lowest and the highest value easily. (range) b. Identify the most frequently occurring value easily. (mode) c. Identify the central value easily. (median) c. Frequency Distribution Table 1.A summary table that divides quantitative data
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