Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent returnfor Vanguard Total Stock Index (all stocks). Let y be arandom variable representing annual return for Vanguard BalancedIndex (60% stock and 40% bond). For the past several years, we havethe following data.
| x: | 21 | 0 | 35 | 27 | 34 | 18 | 37 | −17 | −21 | −20 |
| y: | 16 | −7 | 21 | 20 | 16 | 15 | 17 | −1 | −8 | −8 |
(a) Compute Σx, Σx2, Σy,Σy2.
(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.)
(c) Compute a 75% Chebyshev interval around the mean for xvalues and also for y values. (Round your answers to twodecimal places.)
Use the intervals to compare the two funds.
75% of the returns for the balanced fund fall within a narrowerrange than those of the stock fund.75% of the returns for the stockfund fall within a narrower range than those of the balancedfund.    25% of the returns for the balancedfund fall within a narrower range than those of the stock fund.25%of the returns for the stock fund fall within a wider range thanthose of the balanced fund.
