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Ryerson University
Quantitative Methods
QMS 102
Sheila Rosenberg

Alyssa Soubliere September 16, 2013 Ryerson University QMS102 Lecture Two Notes LectureTwo Notes Graphical Presentation of Qualitative Data  We cannot perform calculations of qualitative (nominal or ordinal) data, but…  You can perform calculations on the number of responses in each category  To graphically present qualitative data we use: o Bar charts (horizontal or vertical) o Pie Charts o Pareto Charts (look like bar charts, but with an additional piece of information)  See example 2.2, 2.3 & 2.4 on pg. 40-43 from textbook  In a bar chart, a bar shows each category, the length represents the amount, frequency or percentage of values falling into a category which come from the summary table of the variable  A pie chart is a circle broken into segments that represent categories. The size of each slice of the pie varies according to the percentage in each category  Named after the 19 century Italian economist Vilfredo Pareto whose research discovered that 80% of the wealth is owned by 20% of the population o Generalized as the 80/20 rule o Is a combination of a vertical bar chart, where categories are shown in descending order of frequency and a cumulative polygon shown in the same graph o Is used to separate the vital few from the trivial many o A Pareto chart, besides the frequency/percentage one also needs a cumulative percentage (has to add up to 100) Graphical Presentation of Quantitative Data  A Stem-and-Leaf Plot is an easy way to o Summarize the distribution (or shape) of quantitative data o See where the concentration of quantitative data exist o Retain most of the data values (numbers) o Is used if the data has no more than 50 values  We start by separating the sorted data series into leading digits (the stems) and the trailing digits (the leaves)  The decimal system is the most common base for representation of numbers  We use numbers 0,1,2,3,4,5,6,7,8,9 to represent integers, fractions, and real numbers  9765= 9*10^3 + 7*10^2 + 6*10^1 + 5  9,765= 9 + 7 * 10^-1 + 6 * 10 ^-2 + 5 * 10^-3  If we have a data value 84 we can take a stem (in units of 10) to be 8 and a leaf to be 4 since 84 = 8 * 10 + 4  If we have a data value 13000 we can take a stem (in units of 10000) to be 1 and a leaf to be 3 since 13000 = 1*10^4 + 3*10^3 Alyssa Soubliere September 16, 2013 Ryerson University QMS102 Lecture Two Notes Stem-and-Leaf Plot Rules:  The Stem Rules: 1. The number of stems should be from 6 to 13 2. Stem values should
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