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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 twoweek
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. (xx) ()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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 Spring '10
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 Standard Deviation, decimal places, Shawn Pan'ini

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