Do bonds reduce the overall risk of an investment portfolio? Letxbe a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Letybe a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

x:	36	0	12	37	18	17	15	20	11	19
y:	26	8	26	21	24	12	21	10	4	1

(a) Computex,x²,y,y².

x		x2
y		y2

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation forxand fory. (Round your answers to four decimal places.)

	x	y
x
s2
s

(c) Compute a 75% Chebyshev interval around the mean forxvalues and also foryvalues. (Round your answers to two decimal places.)

	x	y
Lower Limit
Upper Limit

(d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.)

	x	y
CV	%	%

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set16,4,8,13,14.(a) Use the defining formula, the computation formula, or a calculator to computes. (Round your answer to four decimal places.) s= (b) Multiply each data value by7to obtain the new data set112,28,56,91,98. Computes. (Round your answer to four decimal places.) s=

Given 1 mile 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) s = km

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.

8, 6, 14, 16, 14

(a)Use the defining formula, the computation formula, or a calculator to computes. (Enter your answer to four decimal places.)

(b)Add3to each data value to get the new data set11,9,17,19,17. Computes. (Enter your answer to four decimal places.)