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QMS102(3)-S11.doc

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Department
Quantitative Methods
Course
QMS 102
Professor
anon
Semester
Summer

Description
Session 3 (June 30) Another example (Page 72) Consider the following frequency distributions of manufacturing personnel salaries at ABC and XYZ Inc. Salary ($000’s) ABC Inc. # XYZ Inc. # of employees of employees 20 and under 25 24 10 25 and under 30 41 23 30 and under 35 44 31 35 and under 40 29 14 40 and under 45 15 8 45 and under 50 7 2 Note that there is a large difference in the number of employees in the two companies. So it is difficult to compare the salary distribution by looking at the frequencies. We need to set up a relative frequency or percentage distribution for two sets of salaries. Relative Frequency of a class • Portion or percentage of the data that falls in a particular class. f • The relative frequency, rf, is given byf n, where f is the class frequency and n is the sample size. Summer2011 Page1 Example 1. The following sample data set lists the number of minutes 50 Internet subscribers spent on the Internet during their most recent session. Construct a frequency distribution following the rule in the text. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 86 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44 The following was obtained by using CW=10. You may do so by using CW=20. # Minutes they spent # of Subscribers rf 0 and under 10 2 0.04 10 and under 20 5 0.10 20 and under 30 7 0.14 30 and under 40 11 0.22 40 and under 50 7 0.14 50 and under 60 9 0.18 60 and under 70 3 0.06 70 and under 80 4 0.08 80 and under 90 2 0.04 Total 50 1.00 Another example (Continued) Salary ($000’s) ABC ABC XYZ XYZ f rf f rf 21 and under 25 24 0.150 10 0.114 26 and under 30 41 0.256 23 0.261 31 and under 35 44 0.275 31 0.352 35 and under 40 29 0.181 14 0.159 40 and under 45 15 0.094 8 0.091 45 and under 50 7 0.044 2 0.023 Total 160 1.000 88 1.000 Summer2011 Page2 Summer2011 Page#3 One question cannot be answered using the relative frequency distribution Example: The following sample data set lists the number of minutes 50 Internet subscribers spent on the Internet during their most recent session. Construct a cumulative frequency distribution. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 86 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44 Question: How many subscribers in percentage spent less than 57 minutes on the Internet? Summer2011 Page4 Summer2011 Page#5 Steps for constructing an Ogive Summer2011 Page#6 Example: Constructing a Cumulative Frequency Distribution and Draw an OGIVE. The following sample data set lists the number of minutes 50 Internet subscribers spent on the Internet during their most recent session. Construct a cumulative frequency distribution. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 86 41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20 18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44 # Minutes they spent f rf crf 1 and under 10 2 0.04 0.04 11 and under 20 5 0.10 0.14 21 and under 30 7 0.14 0.28 30 and under 40 11 0.22 0.50 40 and under 50 7 0.14 0.64 50 and under 60 9 0.18 0.82 60 and under 70 3 0.06 0.88 70 and under 80 4 0.08 0.96 80 and under 90 2 0.04 1.00 Total 50 1.00 Use Excel, we can obtain the following Ogive: Internet Usage 190 80 70 60 40 30 The cumulative (%) 10 0 10 20 30 40 50 60 70 80 90 The # of minutes Summer2011 Page#7 Use the above Ogive, we can estimate there were 39 users (78%) spending less than 57 minutes on the Internet. EXAMPLE : The frequency-distribution table shown below summarizes 1200 grades received on 4 examinations by 10 sections of 30 students each. The first column lists the ten classes (intervals) into which th
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