Let x be the random variable representing annual percent return for the Vanguard

Question

Let x be the random variable representing annual percent return for the Vanguard Total Stock Index (stocks only). Let y be a random variable representing annual return for a balanced index (60% stocks and 40% bonds). The standard deviations of x and y are 20.86 and 12.15, respectively. Answer the following questions related to this table:

a) Find the mean of the x values.

b) Find the mean of the y values.

c) Compute an 89% Chebyshev interval around the mean of the y values.

d) Find the Coefficient of Variation for x to one decimal place.

e) Find the Coefficient of Variation for y to one decimal place.

e) Which of x or y seems to have the greater spread about the mean? Explain

Explanation / Answer

Solution:

Solution(a) Mean value of X = (13+0+36+22+32+24+25-13-13-22)/10 = 104/10 = 10.4

Solution(b) Mean value of Y = (7-2+27+16+23+17+16-2-3-7)/10 = 92/10 = 9.2

Solution(c)

1 - 1/k^2 = 0.89

-1/k^2 = -0.11

K^2 = 1/0.11 = 9.0909

K = 3.01

Mean +/- K*SD

9.2 +/-3.01 *12.15

-273715 to 45.7715

Solution(d) Coeficient of variation = (SD/mean)*100% = (20.86/10.4)*100% = 200.57%

Solution(e) Coeficient of variation = (SD/mean)*100% = (12.15/9.2)*100% = 132.0652%

Solution(f) As we can see that Coeficeint of variation of X is more than Y so Y seems to have greater spread about the mean.

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