3-3 example8 - Student: Grady Sinlonton Colu'se:...

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Unformatted text preview: Student: Grady Sinlonton Colu'se: 1\-Iat11119: Elementary Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: Triola: Elementary Statistics. 11e Time: 11:53 AM Listed below are costs (in dollars) of roundtrip flights between two cities. All flights involve one stop and a two-week stay. Find the coefficient of variation for each of the two sets of data, then compare the variation. 30DaysinAdvance:335 315 230 330 234 321 294 lDayinAdvance: 455 640 557 1,055 588 1,155 574 S _ The coefficient of variation is given as CV = r - 100%, where s is the sample standard deviation, and x is the sample it me an. First, calculate the sample means. The mean, ;, ofa sample is found with the formula below, where x is the variable used to represent the individual data values, and n is the number of data values in the sample. 2x (— sum ot‘all data values x = n (— number ot data values Let x] be the prices of tickets purchased 30 days in advance. Calculate a, rounding to three decimal places. E, = 294.143 Let x2 be the prices of tickets purchased 1 day in advance. Calculate ;2, rounding to three decimal places. {2:7'17'3'14 Next, calculate the sample standard deviations. l — 2 x - x — The standard deviation, s, of a sample is found by using the formula s = fl—l) _, where x is the mean of the n _ sample, and n is the size of the sample. For x I, calculate the first value of (x - i). (335 — 294.143) 40.85? (x—E) Calculate (x - i) for the remaining data values. Page 1 Student: Grady Sinlenten Celu'se: 1\-Iat11119: Elenlentaiy Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Beck: T1‘iela: Elenlentaiy Statistics. Me Time: 11:53 AM — 2 . . . Calculate (x - x) tor the first data value, rounding to four dec1mal places. (x — ;) 2 = (335 — 294.143)2 = (40.85?) 2 = 16692944 Calculate (x — 2 for the remaining data values, rounding to four decimal places. ('x— x) (x —;)Z 40.35 16692944 20.857 435.0144 — 64.143 4114.3244- 3535712857244 — 60.143 36111804 26.857 721.2984 — 0.143 0.0204 Now find the sum of the values of (x - 2. 2(x —§)2=11,s42.8568 Finally, divide the sum of the values of (x — 2 by (n - 1) to find the variance, where n is the sample size. Then take the square root to find the standard deviation, rounding to three decimal places. 3. = 1 201—302 n—l = 111,842.8568 7—] = 1;} 1,9?38095 = 44.428 Page 3 Student: Grady Sinlonton Colu'se: 1\-Iat11119: Elenlentaiy Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: T1‘iola: Elenlentaiy Statistics. Me Time: 11:53 AM Repeat the calculations for the other sample. Recall that the mean of x2 is ?l?.?l4. Calculate (x - E) for the data values. Calculate (x — 2 for the data values ofxg, rounding to four decimal places. (x-x) ()4; -§)2 —262.?14 690186458 — 77.714 6039.4658 — 160.714 253289898 337.286113?61.3458 — 129314- 168253218 437.286 1912190458 — 143.714 206533138 Now find the sum ofthe values of (x — 2. 2(x — E) 2 = 443,347.4286 Finally, divide the sum of the values of (x — 2 by (n - l) to find the variance, where n is the sample size. Then take the square root to find the standard deviation, rounding to three decimal places. — 2 s] = libs—vi) n—l = ’443,347.4286 7—1 = t] 3733912381 = 2?l.829 Now that s and ; have been calculated for both data sets, the coefficient of variation can be found and the variations can be compared. Page 3 Student: Grady Sinlonton Colu'se: 1\-Iat11119: Elenlentaiy Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: T1‘iola: Elenlentaiy Statistics. Me Time: 11:53 AM S _ Recall that the coefficient of variation is given as CV = r : 100%, where s is the sample standard deviation, and x is the x sample mean. Calculate the coefficient of variation for the two samples, rounding to three decimal places. 5 S CV1 = _—' 100% (:v2 = _—2 100% x1 x2 44.428 2?].829 =—-100% =—-100% 294.143 111714 = 15.104% = 37.8?4% When comparing variation in two different sets of data, the standard deviation should be compared only if the two sets of data use the same scale and units and they have the same mean. If the means are substantially different, or if the samples use different scales or measurement units, use the coefficient of variation to compare the variation in the data. Page 4 ...
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This note was uploaded on 05/21/2010 for the course MATH 49239 taught by Professor Parvini during the Spring '10 term at Mesa CC.

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3-3 example8 - Student: Grady Sinlonton Colu'se:...

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