Q1. What are the median and the third quintile of the following data points, respectively?

9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%

A)   13.1%; 13.7%.

B)   13.1%; 13.6%.

C)   12.8%; 13.6%.

Q2. What is the seventh decile of the following data points?

81     84    91    97    102           108           110           112           115           121

128     135           138           141           142           147           153           155           159           162

A)   141.0.

B)   142.0.

C)   141.7.

Q3. What does it mean to say that an observation falls in the sixty-fifth percentile?

A)   65% of all the observations are below that data point.

B)   35% of all the observations are above that data point.

C)   65% of all the observations are above that data point.

Q4. Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:

A)   23%.

B)   21.5%.

C)   20.0%.

Q5. One year ago, an investor made five separate investments with the invested amounts and returns shown below. What is the arithmetic and geometric mean return on all of the investor’s investments respectively?

Investment       Invested Amount      Return (%)

A                      10,000             12

B                   10,000            14

C                   10,000             9

D                 20,000             13

E                   20,000             7

A)   11.64; 10.97.

B)   11.00; 10.78.

C)   11.00; 10.97.

答案和详解如下：

Q1. What are the median and the third quintile of the following data points, respectively?

9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%

A)   13.1%; 13.7%.

B)   13.1%; 13.6%.

C)   12.8%; 13.6%.

Correct answer is A)

The median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7^th term.

The formula for determining quantiles is: L_y = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8^th and 9^th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 − 0.136) = 0.1372, or 13.7%.

Q2. What is the seventh decile of the following data points?

81     84    91    97    102           108           110           112           115           121

128     135           138           141           142           147           153           155           159           162

A)   141.0.

B)   142.0.

C)   141.7.

Correct answer is C)

The formula for determining quantiles is: L_y = (n + 1)(y) / (100). Here, we are looking for the seventh decile (70% of the observations lie below) and the formula is: (21)(70) / (100) = 14.7. The seventh decile falls between 141.0 and 142.0, the fourteenth and fifteenth numbers from the left. Since L is not a whole number, we interpolate as: 141.0 + (0.70)(142.0 − 141.0) = 141.7.

Q3. What does it mean to say that an observation falls in the sixty-fifth percentile?

A)   65% of all the observations are below that data point.

B)   35% of all the observations are above that data point.

C)   65% of all the observations are above that data point.

Correct answer is A)

If the observation falls at the sixty-fifth percentile, 65% of all the observations fall below that data point.

Q4. Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:

A)   23%.

B)   21.5%.

C)   20.0%.

Correct answer is A)

The third quartile is calculated as: L_y = (7 + 1) (75/100) = 6. When we order the observations in ascending order: 7%, 10%, 12%, 15%, 20%, 23%, 27%, “23%” is the sixth observation from the left.

Q5. One year ago, an investor made five separate investments with the invested amounts and returns shown below. What is the arithmetic and geometric mean return on all of the investor’s investments respectively?

Investment       Invested Amount      Return (%)

A                      10,000             12

B                   10,000            14

C                   10,000             9

D                 20,000             13

E                   20,000             7

A)   11.64; 10.97.

B)   11.00; 10.78.

C)   11.00; 10.97.

Correct answer is C)

Arithmetic Mean: 12 + 14 + 9 + 13 + 7 = 55; 55 / 5 = 11

Geometric Mean: [(1.12 × 1.14 × 1.09 × 1.13 × 1.07)^1/5] − 1 = 10.97%

Q6. The following data points are observed returns.