Chebyshev's Theorem: Analyzing Investment Portfolio Risk

[cyod22]

1. do bonds reduce the overall risk of an investment portfolio? let x be a random variable representing annual % return for Vangaurd Total Stock Index (all stocks). Let y be a random variable representing annual return for Vangaurd Balanced Index(60% stock and 40% bond). For the past several years we have the following data.

x: 11 0 36 21 31 23 24 -11 -11 -21
y: 10 -2 29 14 22 18 14 -2 -3 -10

a.) Compare Ex, Ex2, Ey and Ey2 (2 = squared)

b.) use results in part (a) to compute the sample mean, variance, and standard deviation for x and for y.

c.) Compute a 75 % Chebyshev interval about the mean for x values and also for y values. Use interval to compare funds.

I was able to do part a & b but have no idea what they want for c. i do have the answer but i am not sure what they used to get the answer.

Homework Equations

The Attempt at a Solution

 

[vela]

What is a Chebyshev interval?

 

[statdad]

There are two possibilities - I'm not sure what level of work you're at.

First (and simplest): how many standard deviations around the mean does chebyshev's theorem say you must go to include 75% of the data values? (remember chebychev's theorem says the percentage of values between $$\bar x \pm ks$$ is at least
$$1 - {1}/{k^2}$$.

Second (and more complicated) is the idea discussed at the following link:
http://www.quantdec.com/envstats/notes/class_12/ucl.htm

I'm guessing it is option 1 you need to use.