chapter 1

Chapter 1: Overview and Descriptive StatisticsSection 1.444.a. range = 49.3 – 23.5 = 25.8b.x ( x i− x)i2( x i− x)29.5 -1.53 2.3409 870.2549.3 18.27 333.7929 2430.4930.6 -0.43 0.1849 936.3628.2 -2.83 8.0089 795.2428.0 -3.03 9.1809 784.0026.3 -4.73 22.3729 691.6933.9 2.87 8.2369 1149.2129.4 -1.63 2.6569 864.3623.5 -7.53 56.7009 552.2531.6 0.57 0.3249 998.56Σx = 310.3 Σ( x i− x)= 0 Σ(x )2 i− x = 443. 801 Σ( x2 ) = 10,072. 41i2xixs2= 31.03nΣ(x − )1= = ixin − 12443.801= = 49.311292c. s = s = 7 . 02222 222 Σx− ( Σx)/ n 10,072.41−(310.3)/10d. s === 49. 3112n −1945.1a. x =n ∑ x i= 577.9/5 = 115.58. Deviations from the mean:i116.4 - 115.58 = .82, 115.9 - 115.58 = .32, 114.6 -115.58 = -.98,115.2 - 115.58 = -.38, and 115.8-115.58 = .22.b. s 2 = [(.82) 2 + (.32) 2 + (-.98) 2 + (-.38) 2 + (.22) 2 ]/(5-1) = 1.928/4 =.482,so s = .694.c. ∑ix 2 i= 66,795.61, so s 2 =1n−1⎡⎢⎢⎣23∑i2⎤2 ⎛ ⎞1xi−n⎜∑xi⎟ ⎥ =⎝ i ⎠ ⎥⎦[66,795.61 - (577.9) 2 /5]/4 = 1.928/4 = .482.d. Subtracting 100 from all values gives x =15. 58 , all deviations are the same as inpart b, and the transformed variance is identical to that of part b.