103 80 up to 90 2 90 up to 100 7 100 up to 110 6 110 up to 120 9 120 up to 130

103 80 up to 90 2 90 up to 100 7 100 up to 110 6 110

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103 80 up to 90 2 90 up to 100 7 100 up to 110 6 110 up to 120 9 120 up to 130 8 130 up to 140 7 140 up to 150 3 150 up to 160 3 TOTAL 45 Number of Spots Purchased Frequency Frequency Distribution Example 102
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Stem-and-leaf Plot Example 103 88 89 96 93 95 96 94 94 97 108 107 103 104 106 103 Stem-and-leaf: Another Example (Minitab) 104
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z The standard deviation is the most widely used measure of dispersion. z Alternative ways of describing spread of data include determining the location of values that divide a set of observations into equal parts. z These measures include quartiles, deciles, and percentiles. Quartiles, Deciles and Percentiles 107 LYING with Statistics Often Just Misstatement / Misunderstanding of Terminology: z 92% on Test = “In Top 10% of Class” INSTEAD = “Top 10% of Possible Points” z 92 nd Percentile = “Twice as High as 46 th” INSTEAD = “92 nd Percentile scored better than twice as many people as the 46 th
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Visualizing Quartiles / Percentiles Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ Ɣ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 z To formalize the computational procedure, let L p refer to the location of a desired percentile. So if we wanted to find the 33rd percentile we would use L 33 and if we wanted the median, the 50th percentile, then L 50 . z The number of observations is n, so if we want to locate the median, its position is at ( n + 1)/2, or we could write this as ( n + 1)( P /100), where P is the desired percentile. Percentile Computation 108
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Percentiles - Example Listed below are the commissions earned last month by a sample of 15 brokers at Salomon Smith Barney’s Oakland, California, office. $2,038 $1,758 $1,721 $1,637 $2,097 $2,047 $2,205 $1,787 $2,287 $1,940 $2,311 $2,054 $2,406 $1,471 $1,460 Locate the median, the first quartile, and the third quartile for the commissions earned. 108 Percentiles – Example (cont.) Step 1: Organize the data from lowest to largest value $1,460 $1,471 $1,637 $1,721 $1,758 $1,787 $1,940 $2,038 $2,047 $2,054 $2,097 $2,205 $2,287 $2,311 $2,406 108
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Percentiles – Example (cont.) Step 2: Compute the first and third quartiles. Locate L 25 and L 75 using: 205 , 2 $ 721 , 1 $ 12 100 75 ) 1 15 ( 4 100 25 ) 1 15 ( 75 25 75 25 . . L L L L ly respective positions, 12th and 4th the at located are quartiles third and first the Therefore, 108 Box Plot - Data Needed 111 A Box Plot needs 5 pieces of data: z Minimum Value - Lower Tail z Q1 (25th Percentile) - Lower Box z Median (Q2 or P50) - Middle of Box z Q3 (75th Percentile) - Upper Box z Maximum Value - Upper Tail
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Box Plot - Example 111 Box Plot Example Step1: Create an appropriate scale along the horizontal axis. Step 2: Draw a box that starts at Q1 (15 minutes) and ends at Q3 (22 minutes). Inside the box we place a vertical line to represent the median (18 minutes). Step 3: Extend horizontal lines from the box out to the minimum value (13 minutes) and the maximum value (30 minutes). 111
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Box Plot – Using Minitab Develop a box plot of the data for the data below from Chapter 2. What can we conclude about the distribution of the vehicle selling prices?
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