Question

The dela sel below on the left represents the annual rale of relurn fin percent of eight randorrly Barnped bond mutual funds, and the cale sal (a) Determine the mean and slancard cevision of each dala el. below on the right represents the annual rate of retum in percent) of eight randomy sampled stock mutual funds. Use the information in the table below to complete pars (a) through (d). Then complena part() The mean of the data set for bond mutual funds is (Type an inleger or decirl rounded to three decimal places as neered.) Bond mutual Stock mutual funde funde The standard deviation of the data set for bond mutual funds is. 3.3 1.9 9.5 7.7 (Type an integer or decimal rounded to three decimal places is needed. 2.0 3.5 9.2 7.5 gon 2.5 8.5 7.3 The mean of the data set for stock mutual funds is 3 1.7 2.1 3.2 7.0 (Type an inagar or decimal raunded to three decimal places as needed The elandard devialion of the data del for slack mutual funds is (Type an integer or dacimal rounded to three decimal places es nesced (6) Based only on the standart.deviation, have more spread. (c) What proportion of the bard inutual funds are within one stardard deviation of the mean? (Type an integer or decimal rounded to three decimal places as needed.) Whal proportion of the clock inulusal furies are willin one standard devia.on of the mean? (Type an integer or decitral rounded to three decimal places as necced.) (d) The coefficient of variation, CV, is defined as the ratio of the standard deviation to the mean of a cale sel stardard deviation CV- meen The CV allows for a comparison in spread by describing the amount of spread por unit maen Compute the CV for both data sets. What is the CV af the data set for bond mutual funds? (Typa an inagar or decimal rounded to three decimal places as needed What is the CV of the data sel for slack mutual funds? M (Type an integer or decimal rounded to three decimal places na necred.) Based on the coefficieril of variation, trave more spread.

Answer 1

a) For bond mutual Funds:

∑x = 19.8

n = 8

∑(x-x̅)² = 3.135

Mean, x̅ = Ʃx/n = 19.8/8 = 2.475

Standard deviation, s = √(Ʃ(x-x̅)²/(n-1)) = √(3.135/(8-1)) = 0.669

For stock mutual Funds:

∑x = 64.9

n = 8

∑(x-x̅)² = 5.70875

Mean, x̅ = Ʃx/n = 64.9/8 = 8.113

Standard deviation, s = √(Ʃ(x-x̅)²/(n-1)) = √(5.7088/(8-1)) = 0.903

b)

Based on Standard deviation, Stock mutual fund has more spread.

c)

Proportion for bond mutual fund = 5/8 = 0.625

Proportion for stock mutual fund = 5/8 = 0.625

d)

CV for bond mutual fund = s/x̅ =  0.669/2.475 = 0.270 = 27.0%

CV stock mutual Funds = s/x̅ =  0.903/8.113 = 0.111 = 11.1%

Based on CV, bond mutual fund has more spread.

e)

In inches:

∑x = 568

n = 8

∑(x-x̅)² = 86

Mean, x̅ = Ʃx/n = 568/8 = 71.000

Standard deviation, s = √(Ʃ(x-x̅)²/(n-1)) = √(86/(8-1)) = 3.505

In centimeter:

∑x = 1442.72

n = 8

∑(x-x̅)² = 554.8376

Mean, x̅ = Ʃx/n = 1442.72/8 = 180.340

Standard deviation, s = √(Ʃ(x-x̅)²/(n-1)) = √(554.8376/(8-1)) = 8.903

Based on Standard deviation, height in centimeter has more spread.

CV for inches = s/x̅ =  3.505/71 = 0.049

CV for centimeter =8.903/180.34 = 0.049