The accompanying data sets represent the annual rate of return (in percent) of e

Question

The accompanying data sets represent the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the annual rate of retum (in percent) of eight randomly sampled stock mutual funds. Use the information in the table below to complete parts (a) through (d). Then complete part (e Click the icon to view the data. (a) Deternine the mean and standard deviation of each data set. i Data Table The mean of the data set for bond mutual funds 3 Type an integer or decimal rounded to three decimal places as needed.) The staridard deviation of the data set for bond mutual funds is Type an integer or decimal rounded to three decimal places as needed.) Bond mutual funds 3.0 1.6 1.7 3.2 2.2 2.5 1.4 1.8 Stock mutual funds 9.2 74 8.9 72 8.2 7.0 7.9 6.7 The mean of the data set for stock mutual funds is Type an integer or decimal rounded to three decimal places as needed.) The standard deviation of the data set tor stock mutual funds is Type an integer or decimal rounded to three decimal places as needed.) Print Done (b) Based on only the standard devlation, which data set has more spread? Based only on the standard deviation, have more spread.

Explanation / Answer

a)

Ans : Bond data, Mean = 2.175

Ans: Bond data, Standard deviation = 0.626

Ans: Stock data, Mean = 7.813

Ans: Stock data, Standard deviation = 0.845

b)

Based on only standard deviations, Stock mutual funds data has more spread.

c)

The proportion of Bond data that lies within : 2.175 - 0.626, 2.175 + 0.626 = 1.549 to  2.801

Ans: 5/8 or 0.625

The proportion of Stock data that lies within : 7.813 - 0.845, 7.813 + 0.845 = 6.968 to 8.658

Ans: 5/8 or 0.625

d)

CV for Bond data set : 0.626 / 2.175 = 0.288

CV for Stock data set : 0.845 / 7.813 = 0.108

Based on the CV, the Bond data set has more spread.

e)

Mean for Height in inches = 71

Standard deviation for Height in inches = 3

Mean for Height in cm = 180.34

Standard deviation for Height in inches = 7.62

CV for height in inches = 3/71 = 0.0422

CV for height in cm = 7.62/180.34 = 0.0422

Ans : (A) When converting units of measure, the CV is unchanged (As we have seen, the constant gets cancelled out and two values in different units but the same physical quantity will give us the same CV as the constant gets cancelled out in the ratio of Mean to SD)

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