Standard deviation

# Standard deviation - STS 2610 Quantitative Methods Spring...

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Unformatted text preview: STS 2610: Quantitative Methods Spring 2014 JQHWAM 21 lUl‘i’ More on the Standard Deviation ifr r Example: Dr. Kramer gives weekly quizzes (10 questions, 5 points each, no partial credit) in his probability class. The score distribution for last week's quiz is given below. sampir dmanm = 31 ._ 20(st h‘l F a. Calculate the median quiz score. - ram.“ [ha-“3%! ' 53-5 (W a; 53‘“) WOMN’ 40 mOdf‘ 40 b. Calculate the mean quiz score. y M‘ 25 ”“5" '1 '35 23 . +052 445 m .50: a319,: “4 ’7‘ c. Calculate the standard deviation of the quiz scoresa 5‘»-~ 0.1 c it)“ 1 0.13154193002 sﬁgﬁ-élﬁ’ﬂ) . . (510-5? (31(3) N H} . . . e 1 : -. > ‘ W O" 5.723;“: 4533 7 : Q‘VO Wells Fargo Banks call center has representatives that can speak English and Spanish. The lengths (seconds) of a sample of 11 calls in which English was spoken are given below along with the lengths of 14 calls conducted in Spanish. mmmmmnnmmmm mnmm 151 127 147 mammalian-alg- Engiish: mean = Y ' 1H3? standard deviation = 5'- 2141 Spanish: mean = 1 2 ISO at standard deviation = 3= 20 .‘ﬂ Which group has the more variable call lengths? Spamlh ' in iaiqcrsiandard dcm’ahm (mb'lrt' van'ahm) Fiﬁ [Mint van‘a mm”? 7‘ : 22.42 W i coefﬁcient ofvariation - CV1 3-75-(IM) CV: " I”. 3.? (‘0‘) ‘ 80 3%]. Li Gamma) dt’v C\i=,%:Uw) CV3: 2".”rLIw): new]. E -/, 0‘ man Thm S10Hd01d 150.81: . J vanah‘cn it’laM 0040116" '5 7’ mifai‘ﬁf‘ man Exercise: Data for samples from muiti-vitamin tablets from two manufacturers are given below. Prescott Pharmaceuticals Vitacorp 500 mg 250 mg n = 100 n=200 . i=500.02 i=249.03 Nana (V s=10.3 s=7.9 '\ 7‘ lw variation, mm conststm’t Which manufacturer appears to have a more consistent manufactﬁ'ing process? - l.5 . _ ' q. ’ . ~.\ 0’? 3%551 (HID ‘ 1'0“" CV; 21509050“ LajPCC/ man—“Man X-Y . - , any Jig- Wmmrmrni—mmn 2: x ‘5? it‘lls hiwm (Siamlaidrirdvalut) (1“,.qu swam a 5 -» Standard dt‘v abovc . Imam 2 :m or bclow am a *WWW 0‘ mraswcmmi ans .v... cmpi'tffou Ruif { i More Information from the Standard Deviation: 17/.” 2‘7, , Emp'nca' Rule ' J I i N“ A4.— Afar “'5" N» K" H316 N" 1- “PPM 08/. 04 mt’wmcmrm at dasin'ommn fan WW“ ' Simdaid dz‘wanm ct 1hr mm C“) (A. (MU?) 2-099“ “‘5"- 0" mrmmcmmu win tan “4'" Z “Gilda“! dmahm a mm” (m 20’. Any) 3. 7. max-M71. ‘ 35iandaid dm‘am (ﬁx-3r 11'5““) "scar“ , _; a” a 5115* use we \“"V'll 515- @440 Example: 9 us a. 56 w 7“ 0 Suppose that the distribution of SAT math scores for last year was approximatelng with W33" score u z 515 and standard deviation 0 s 115. — M What proportion of scores fall between 285 and 745? 0m Whatproport‘iotnnotﬁorfssfilajogizﬁoi : l i 33' ”(~0ny “Wk 5 2. '2— __/ a What proportion of scores fall below 285? a 51' Egg; 5/1.: 2151-5 5 5, . ‘ '(b’q 2" '. a. I ‘ Whatproportionof scores fall between {3553 “3’02 "'1’ 7. 3+1. \$235.... What proportion of scores falquetween 630 and 745? . 415 \ Eli-"Asqoga'g' ” ;~ raise-51%.:,-i-;:~'--".-‘.'i 7“ ' a i :1: 4' 9 E“. ‘. ~— %ﬂf’———m ' ' ii at 5M2!“ ' 9;. 145 . WW K smndmd dwahm “mm" iguana mm matrix at mcaswrmcmi “NM m“ l- i1 ' to! 5 mm 2' (lob-Liz 75/. -0H(aiH\$"-'"15d' a. mi - w mum 1“ “d . - . {an 4. (My at rrm» (HI Milt {n 4: Siahda'd mom“ . .. . . . . [w x W: Suppose that tuition and fees at colleges and universities in the US. follow a distribution / ‘00 with ma u = \$16,500 and standard deviation 0 = \$10,000. a—I”. "' ‘ At least 15 96 of US. colleges and universities have tuitionsmuhan \$36,500. ( 0: 59'5’3 I *6‘ A: most 96 of US. colleges and universities have tuitions W 546500? 5:: “.93 759,500 ”0'”- ngl’ m 50.5% - M00" (1 “J l “(f "(3" “0’ 3 mum «A, 33 m- ...
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