9、Given the following annual returns, what is the range?

A)  22.0%.

B)   15.0%.

C)   (7.0)%.

D)   3.0%.

10、For the past three years, Acme Corp. has generated the following sample returns on equity (ROE): 4 percent, 10 percent, and 1 percent. What is the sample variance of the ROE over the last three years?

A)   4.6%.

B)   21.0(%²).

C)   5.0(%²).

D)   21.0%.

11、Given the following annual returns, what are the population variance and standard deviation, respectively?

A)              32.4                                5.7

B)              22.0                                4.7

C)              51.6                                7.2

D)               64.5                              8.0

12、When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful? The

A)   variance.

B)   median.

C)   standard deviation.

D)   mode.

答案和详解如下：

9、Given the following annual returns, what is the range?

2000	2001	2002	2003	2004
15%	2%	5%	(7%)	0%

A)  22.0%.

B)   15.0%.

C)   (7.0)%.

D)   3.0%.

The correct answer was A)

Range = Highest Value – Lowest Value. 15% - (7%) = 22.0%.

10、For the past three years, Acme Corp. has generated the following sample returns on equity (ROE): 4 percent, 10 percent, and 1 percent. What is the sample variance of the ROE over the last three years?

A)   4.6%.

B)   21.0(%²).

C)   5.0(%²).

D)   21.0%.

The correct answer was B)

[(4 - 5)² + (10 - 5)² + (1 - 5)²] / (3 - 1) = 21(%²).

11、Given the following annual returns, what are the population variance and standard deviation, respectively?

2000			2001	2002	2003		2004
15%			2%	5%	-7%		0%.
		Population Variance				Standard Deviation

A)              32.4                                5.7

B)              22.0                                4.7

C)              51.6                                7.2

D)               64.5                              8.0

The correct answer was C)

The population variance is found by taking the mean of all squared deviations from the mea

[ (15-3)² + (2-3)² + (5-3)² + (-7-3)² + (0-3)² ] / 5 = 51.6

The population standard deviation is found by taking the square root of the population variance.

51.6^1/2 = 7.2

12、When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful? The

A)   variance.

B)   median.

C)   standard deviation.

D)   mode.

The correct answer was C)

The standard deviation is more useful than the variance because the standard deviation is in the same units as the mean. The median and mode do not help in creating intervals around the mean.