ch6_some_techniques_of_calculation.studentview

Of mean sd no mean sd students students revised mark

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Unformatted text preview: = 76 5 4 SD(Y ) = × 8 = 6.4 5 Similarly, for the 50 students with x < 50 , Similarly, Mean(Y ) = 60 − 11 (50 − 40) = 49 10 SD(Y ) = 11 × 6 = 6.6 10 Hence the mean & s.d. of the 250 new marks can be Hence found from the frequency table: found x 76-6.4= 69.6 82.4 42.4 55.6 55.6 f 100 100 25 25 76+6.4= 49-6.6= 49+6.6= ∴ µ = 70.6, σ = 12.5748 N 250 Simple Exercise: Simple Data set : x , x ,........, x Data Mean=12, Median=14, Mode=15 and CV=30%. Define new data set: yi = 80 − 4 xi i = 1,2,........,80 1 2 80 Find the mean, median, mode, s.d, CV and Sk for the yi ' s . Sk Solution: Solution RULES: RULES Y = a + cX then µY = a + cµ X MedY = a + c ⋅ Med X ModY = a + c ⋅ Mod X σ Y =| c | ⋅σ X and 2 2 σ Y = c 2 ⋅σ X Given and µX =12 C .V X = Med X =14 σX Mod X =15 σX =30% µX = 0.3 12 ∴ X =3.6 σ Y = a + cX Y = 80 − 4 X ⇒ a = 80, c = −4 µY = a + cµ X = 80 − 4 ×12 = 32 MedY = a + c ⋅ Med X = 80 − 4 ×14 = 24 ModY = a + c ⋅ Mod X = 80 − 4 ×15 = 20 σ Y =| c | ⋅σ X = 4 × 3.6 = 14.4 σ 14.4 C.VY = Y = = 45% µY 32 3( µY − MedY ) 3(32 − 24) SkY = = = 1.66667 σY 14.4...
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