Lct02 - Introduction to Business Statistics Lecture 2 Descriptive Statistics II Numerical Methods Example A large manufacturing company in Michigan

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1 Introduction to Business Statistics Lecture 2 Descriptive Statistics II: Numerical Methods Example: A large manufacturing company in Michigan has about 5000 assembly line workers. For training purposes, management needs to know skill level of these workers. A sample of 296 workers has been randomly selected and given an aptitude test with 25 multiple choice questions. The 296 test scores have been arranged in ascending order. What can we say about these 290 observations of scores? Mean: 5777 . 19 296 5795 n X f X i i
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2 Scores ( i X ) Frequency ( i f ) Relative Frequency(%) 0 0.00 1 2 3 4 5 1 0.34 6 7 8 9 0.68 10 1.01 11 12 2.03 13 2.36 14 9 3.04 15 16 18 6.08 17 21 7.09 20 6.76 19 35 11.82 25 8.45 32 10.81 22 30 10.14 23 39 13.18 24 4.05
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3 Scores Frequency 24 21 18 15 12 9 6 40 30 20 10 0 Histogram of Scores
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4 20 2 20 20 2 score 149th score 148th n observatio ranked th 2 1 Median n Explanation : Suppose we have 4 observations 1, 4, 6, 9. Then median is at (4+1)/2 = 2.5 th position – in the middle of 2 nd and 3 rd observations. That is, (4+6)/2 = 5 Mode: The value in a data set that appears most frequently = 23. 20 5 25 Range smallest largest X X First quartile: n observatio ordered th 4 1 1 n Q = 17
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5 Explanation : If we have 8 observations 1, 1.5, 3.5, 5, 5.2, 7.5, 8, 10, then 1 Q is at (8+1)/4=2.25 th position, which is between 2 nd and 3 rd observations and closer to the 2 . In this case, we let 5 . 1 1 Q , the 2 observation. Third quartile: n observatio ordered th 4 ) 1 ( 3 3 n Q = 23 6 17 23 range ile Interquart 1 3 Q Q How would you describe the distribution of scores ? Location Measures of the frequency distribution of scores: Mean, Median (resistance to outliers), Mode Example : Let data be 1, 4, 6, 9. If we change 9 to 1,000,000, what will happen to the mean and median?
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6 Variability Measures of the frequency distribution of scores: Range, Interquartile range, Sample variance, Standard deviation MAD (Mean Absolute Deviation) n X X X X X X n | | | | | | MAD 2 1
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This note was uploaded on 11/23/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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Lct02 - Introduction to Business Statistics Lecture 2 Descriptive Statistics II Numerical Methods Example A large manufacturing company in Michigan

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