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

A)   35% of all the observations are below that point.

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

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

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

2、What is the seventh decile of the following data points?

A)  141.0.

B)   141.7.

C)   142.0.

D)   141.5.

3、What are the median and the third quintile of the following data points?

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%

       Median    Third quintile

A)           13.1 %          13.7 %

B)           13.1 %          13.6 %

C)           12.8 %          13.6 %

D)           12.8 %          13.7 %

4、The following data points are observed returns. 

4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%, 28.1%

What return lies at the seventh decile (70 percent of returns lie below this return)?

A)   17.0%.

B)   18.4%.

C)   19.0%.

D)   16.8%.

5、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?

A)     11.64                                    10.78

B)      1.64                                    10.97

C)      11.00                                  10.78

D)      11.00                                  10.97

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

A)   10.0%.

B)   23%.

C)   20.0%.

D)   21.5%.

答案和详解如下：

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

A)   35% of all the observations are below that point.

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

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

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

The correct answer was C)

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

2、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)   141.7.

C)   142.0.

D)   141.5.

The correct answer was B)

The formula for determining quantiles is: L_y = (n + 1)(y) / (100). Here, we are looking for the seventh decile (70 percent 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.

3、What are the median and the third quintile of the following data points?

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%

       Median    Third quintile

A)           13.1 %          13.7 %

B)           13.1 %          13.6 %

C)           12.8 %          13.6 %

D)           12.8 %          13.7 %

The correct answer was A)

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

The formula for determining quantiles is: L_y = (n + 1)(y) / (100). Here, we are looking for the third quintile (60 percent of the observations lie below) and the formula is: (14)(60)/(100) = 8.4. The third quintile falls between 13.6 percent and 13.9 percent, the eighth and ninth 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%.

4、The following data points are observed returns. 

4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%, 28.1%

What return lies at the seventh decile (70 percent of returns lie below this return)?

A)   17.0%.

B)   18.4%.

C)   19.0%.

D)   16.8%.

The correct answer was B)

The formula for the seventh decile is L_y = (n + 1)(7/10) = 7.70 or between the seventh and eighth return from the left. The seventh return is 17%, while the eighth return is 19%. Interpolating, we find that the seventh decile is 17% + 0.7(19% – 17%) = 18.4%. 成

5、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?

	Investment	Invested Amount		Return (%)
	A	10,000		12
	B	10,000		14
	C	10,000		9
	D	20,000		13
	E	20,000		7
Arithmetic Mean			Geometric Mean

A)     11.64                                    10.78

B)      1.64                                    10.97

C)      11.00                                  10.78

D)      11.00                                  10.97

The correct answer was D)

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%

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

A)   10.0%.

B)   23%.

C)   20.0%.

D)   21.5%.

The correct answer was B)

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.