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Probability - Statistical Methods in Business Professor...

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1 Statistical Methods in Business Professor: Xiaodong Lin Course #: 33:623:385 Office: Levin 252
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2 Statistics and Probability review Descriptive statistics Chapter 2 Probability : Chapter 3 Random variables and sampling: Chapter 4 One sample inferences: Chapter 5 and 6
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3 Sample x 1 ,...,x n Deduction/Probability Induction/Inference Elements Observations Population X 1 ,...,X N
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4 Descriptive Statistics Measures of Location Measures of Variability
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5 Measures of Location Profile Data Set: Sample of 24 Business Stats students’ ages. 18 19 19 19 19 19 20 20 20 20 20 20 20 20 21 21 21 22 22 22 23 24 25 25 Find one number to represent this sample Center of the data Three different ways to measure the center of the data. Mean; Median; Mode
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6 Mean most commonly used measure of central tendency used for quantitative data only sample mean: n x x n i i 1
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7 Median useful when the data has a few extreme data points Median is a more robust statistics then mean To find the median: 1) Sort the data in increasing order 2) If there is an odd number of elements in the data set then Median = middle value If there is an even number of elements in the data set then Median = average of the middle two values
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8 Ex: Number of children 1) Sort data 0 1 1 2 3 2) If there are an odd number of elements then Median = middle value Ex: Number of children (add an element) 0 1 1 2 3 3 3) If there are an even number of elements then Median = average of the middle two values 4) Robustness: 0 1 1 2 3 11 =(1+2)/2=1.5 =1
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9 Mode Mode: most frequently occurring value Ex: Number of Children 0 1 1 2 3 Mode is Ex: Modified A 0 1 1 2 3 3 Mode is 1 1 and 3
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10 Example: students’ ages Profile Data Set: Sample of 24 Business Stats I students’ ages. 18 19 19 19 19 19 20 20 20 20 20 20 20 20 21 21 21 22 22 22 23 24 25 25 Mean Convention: report 1 more decimal place than the data Median Data is sorted Even number of elements so average middle two values: Mode Most frequently occurring value (occurs 8 times) =20.8 =20 =20
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11 Quartiles Quartiles are specific percentiles. First Quartile = 25th Percentile=Q 1 Second Quartile = 50th Percentile = Median =Q 2 Third Quartile = 75th Percentile=Q 3
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12 Example Find quartiles for AGE: Q 1 = , position, i= = Q 3 = , position, i= = Q 2 = median = 20 (25/100)*24 6 (19+20)/2 =19.5 (75/100)*24 18 (22+22)/2 =22
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13 Interquartile Range The interquartile range (IQR) of a data set is the difference between the third quartile and the first quartile. IQR = Q3 Q1 It is the range for the middle 50% of the data. It overcomes the dependency on extreme data values. Group1: Previously calculated: Q1 = 19.5, Q3 = 22 IQR = Group2: Q1 = , Q3 = IQR = 22-19.5=2.5 16 24 24-16=8
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14 Variance The variance is the average of the squared differences between each data value and the mean. If the data set is a sample , the variance is denoted by s 2 .
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