Q5. For the investments shown in the table below, what are the respective mean, median, and mode of the returns?

Investment     Return (%)

A             12

B             14

C              9

D             13

E              7

F              8

G             12

A)         12.00%; 12%; 12%.

B)        10.71%; 9%; 13%.

C)        10.71%; 12%; 12%.

Q6. The owner of a company has recently decided to raise the salary of one employee, who was already making the highest salary in the company, by 40%. Which of the following value(s) is(are) expected to be affected by this raise?

A)    mean and median only.

B)    mean only.

C)    median only.

Q7. An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. Last year, the cash returns was 2.0%, the bonds’ return was 9.5%, and the stocks’ return was –32.5%. What was the return on the investor’s portfolio?

A)   –33.33%.

B)   –16.45%.

C)   –7.00%.

Q8. Given the following annual returns, what are the geometric and arithmetic mean returns, respectively?

2002               2003    2004          2005          2006

15%                 2%      5%             -7%            0%

A)   2.75%; 3.00%.

B)   2.75%; 5.80%.

C)   1.45%; 3.00%.

答案和详解如下：

Q5. For the investments shown in the table below, what are the respective mean, median, and mode of the returns?

Investment     Return (%)

A             12

B             14

C              9

D             13

E              7

F              8

G             12

A)         12.00%; 12%; 12%.

B)        10.71%; 9%; 13%.

C)        10.71%; 12%; 12%.

Correct answer is C)

The mean is the average return computed by summing the returns and dividing by the number of investments: 75 / 7 = 10.71%.

The median is the mid-point or central number of returns arranged from highest to lowest or lowest to highest. In this case: 7, 8, 9, 12, 12, 13, 14. The median return is 12%.

The mode is the return that occurs most frequently. In this case, 12% is also the mode.

Q6. The owner of a company has recently decided to raise the salary of one employee, who was already making the highest salary in the company, by 40%. Which of the following value(s) is(are) expected to be affected by this raise?

A)    mean and median only.

B)    mean only.

C)    median only.

Correct answer is B)

Mean is affected because it is the sum of all values / number of observations.  Median is not affected as it the midpoint between the top half of values and the bottom half of values.

Q7. An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. Last year, the cash returns was 2.0%, the bonds’ return was 9.5%, and the stocks’ return was –32.5%. What was the return on the investor’s portfolio?

A)   –33.33%.

B)   –16.45%.

C)   –7.00%.

Correct answer is B)

Find the weighted mean. (0.10)(0.02) + (0.30)(0.095) + (0.60)(–0.325) = –16.45%.

Q8. Given the following annual returns, what are the geometric and arithmetic mean returns, respectively?

2002               2003    2004          2005          2006

15%                 2%      5%             -7%            0%

A)   2.75%; 3.00%.

B)   2.75%; 5.80%.

C)   1.45%; 3.00%.

Correct answer is A)

Geometric Mean: (1.15 × 1.02 × 1.05 × 0.93 × 1.0)^1/5 − 1 = 1.1454^1/5 − 1 = 2.75%
Arithmetic Mean: (15% + 2% + 5% − 7% + 0%) / 5 = 3.00%

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