Question

X: 19 0 34 35 28 30 24 -24 -8 -13 y: 8 -5 24 22 12 26 9 -9 -2 -4 (a) Compute Ex, Ex2, Ey, Ey? Ex 125 Ex2 5811 Ey 81 Ey2 2151 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.) 12.5 8.1 s 21.73 12.89 (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) Lower Limit -18 X -6.75 Upper Limit 26.25 X 19.5 Use the intervals to compare the two funds. 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 25% of the returns for the stock fund fall within a wider range than those of the balanced fund. (d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.) CV % %

Answer 1

Solution a Gruen that | * | 36) 0 0 116 1-2 * y 4 4 - 9 484 tuฯ 189 906 (76 S7G G) ๆ 57G ๆ 69 ๆ (69 21 - 123 -8 Ex = 581 - 24) 5) any on 4 1 - 1 Ex - 26 = 12.5 1 - 1 - 8) : 8.)

e sample vesicule of mont 2 (u: -)" - (19 - 12.55+ (0-12.5)'* ---+ (13-19.05 ) 10-1. _ _ Is = 472,055 sample variance of y (9: -ýja - (8–8.1) + (-5-8-1)++ -- + [ake 28.1 )? 13 = 166.1 166. - standard deviation of n = 5 I variance I deviation of : 21.73 standard s T 472.05s . variance g = J 166-1 = 12.89

C) According to chehysheus thor at least (e-let) of the neasurement will fall with an (4+* (sp)), u +kx(sp)) like =0.75 k=2 for x; for y → 75%. Chebyshers Internal arand meas : (12.5 -2(21.13) 12.5 +2 (21.73)) - (-30.96,155.96) 754. Chebyshev Intewas around mean (8.1-2 (12-89), 8.1 + $(1299)) - (-17.68, 33-88 ) * opfron a ? Comeet d) Gofficient of variaticis for x = mean (x) = 21.73 - Sd(x) : - 1.74 = 1744. na ~2 12.5 Coefficient & varation for y .sd (1) mean (y) 12.89 8) - 159 -159 y.