Question

The data set below on the left represents the annual rate of return? (in percent) of eight randomly sampled bond mutual? funds, and the data set below on the right represents the annual rate of return? (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

Bond mutual funds

3.1

1.7

1.8

3.3

2.3

2.6

1.5

1.9

Stock mutual funds

9.3

9.0

8.3

8.0

7.5

7.3

7.1

6.8

(a) Determine the mean and standard deviation of each data set.

The mean of the data set for bond mutual funds is nothing. ?(Type an integer or decimal rounded to three decimal places as? needed.) The standard deviation of the data set for bond mutual funds is nothing. ?(Type an integer or decimal rounded to three decimal places as? needed.)

The mean of the data set for stock mutual funds is nothing. ?(Type an integer or decimal rounded to three decimal places as? needed.)

The standard deviation of the data set for stock mutual funds is nothing. ?(Type an integer or decimal rounded to three decimal places as? needed.)

?(b) Based only on the standard? deviation, ? bond mutual funds/ stock mutual funds ___ have more spread.

?(c) What proportion of the bond mutual funds are within one standard deviation of the? mean? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What proportion of the stock mutual funds are within one standard deviation of the? mean? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.

) ?(d) The coefficient of? variation, CV, is defined as the ratio of the standard deviation to the mean of a data set. CV equals StartFraction standard deviation Over mean EndFraction The CV allows for a comparison in spread by describing the amount of spread per unit mean. Compute the CV for both data sets.

What is the CV of the data set for bond mutual? funds? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What is the CV of the data set for stock mutual? funds? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.) Based on the coefficient of? variation, ? bond mutual funds stock mutual funds have more spread.

?(e) In the table? below, the data set on the left has the heights of students measured in? inches, while the data set on the right has the same? students' heights measured in centimeters. For each data? set, determine the mean and the standard deviation. Draw a conclusion about the spread using the standard? deviation, then find the coefficient of variation for both data sets.

Height in inches 68,67,73,65,70,71,70,73

Height in centimeters 172.72,170.18,185.42,165.1,177.8,180.34,177.8,185.42

What is the mean of the data set for height in? inches? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What is the standard deviation of the data set for height in? inches? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What is the mean of the data set for height in? centimeters? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What is the standard deviation of the data set for height in? centimeters? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.) Based on the standard? deviation, the data set for height in ? centimeters inches has more spread.

What is the CV of the data set for height in? inches? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What is the CV of the data set for height in? centimeters? nothing ?(Type an integer or decimal rounded to three decimal places as? needed.)

What is true of the coefficient of? variation?

A. The coefficient of variation is best used when comparing two data sets that use the same units of measure.

B. When converting units of? measure, the coefficient of variation is unchanged.

C. The coefficient of variation does not give as accurate a measurement as the standard deviation

D. The coefficient of variation is always more meaningful than the standard deviation.

Answer 1

a)
For bond mutual funds
mean = 2.275 , std.deviation = 0.669

For stock mutual funds
mean = 7.9125 , std.deviation = 0.903

b)
Based only on the standard? deviation stock mutual funds have more spread.

c)
Proportion for bond mutual funds
mean +/- std.dev = 2.275 +/- 0.669
= (1.606 , 2.944)

Proportion for stock mutual funds
mean +/- std.dev = 7.913 +/- 0.903
= (7.009 , 8.816)

d)
CV for bond mutual funds = std.dev./mean
= 0.669/2.275
= 0.294

CV for stock mutual funds = std.dev./mean
= 0.903/7.913
= 0.114