6、Which of the following statements about the median is FALSE? It is:

A)   more affected by extreme values than the mean.

B)   equal to the 50^th percentile.

C)   a measure of central tendency.

D)   equal to the mode in a normal distribution.

7、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 percent. Which of the following value(s) is (are) expected to be affected by this raise?

A)   median only.

B)   mean and median only.

C)   mean only.

D)   mean, median, and mode.

8、For the investments shown in the table below, what are the mean, median, and mode of the returns?

A)                               10.71%                                       12%                          12%

B)                               12.00%                                       12%                   12%

C)                               11.20%                                       12%                   12%

D)                               10.71%                                       9%                     13%

9、Michael Philizaire is studying for the Level I CFA examination. During his review of measures of central tendency, he decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. Using comparable sales and market data he obtains from a local real estate appraiser, Philizaire calculates the year-to-year percentage change in the value of his home as follows: 20, 15, 0, -5, -5. The geometric return is closest to:

A)   11.60%.

B)   4.49%.

C)   5.00%.

D)   0.00%.

10、Which of the following statements about a normal distribution is least likely accurate?

A)   The mean, median, and mode are equal.

B)   A normal distribution has excess kurtosis of three.

C)   The mean and variance completely define a normal distribution.

D)   Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.

答案和详解如下：

6、Which of the following statements about the median is FALSE? It is:

A)   more affected by extreme values than the mean.

B)   equal to the 50^th percentile.

C)   a measure of central tendency.

D)   equal to the mode in a normal distribution.

The correct answer was A)

Median is less influenced by outliers since the median is computed as the “middle” observation. On the other hand, all of the data including outliers are used in computing the mean. The remaining statements are true regarding the median.

7、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 percent. Which of the following value(s) is (are) expected to be affected by this raise?

A)   median only.

B)   mean and median only.

C)   mean only.

D)   mean, median, and mode.

The correct answer was C)

Mean is affected because it is the sum of all values / number of observations.  Mode is not changed as it measures the value that occurs most frequently.  Median is also not affected as it the midpoint between the top half of values and the bottom half of values.

8、For the investments shown in the table below, what are the mean, median, and mode of the returns?

	Investment		Return (%)
	A		12
	B		14
	C		9
	D		13
	E		7
	F		8
	G		12
		Mean		Median		Mode

A)                               10.71%                                       12%                          12%

B)                               12.00%                                       12%                   12%

C)                               11.20%                                       12%                   12%

D)                               10.71%                                       9%                     13%

The correct answer was A)

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.

9、Michael Philizaire is studying for the Level I CFA examination. During his review of measures of central tendency, he decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. Using comparable sales and market data he obtains from a local real estate appraiser, Philizaire calculates the year-to-year percentage change in the value of his home as follows: 20, 15, 0, -5, -5. The geometric return is closest to:

A)   11.60%.

B)   4.49%.

C)   5.00%.

D)   0.00%.

The correct answer was B)

The geometric return is calculated as follows:

[(1 + 0.20) * (1 + 0.15) * (1 + 0.0) (1 - 0.05) (1 – 0.05)]^1/5 – 1,

or [1.20 * 1.15 * 1.0 * 0.95 * 0.95]^0.2 – 1 = 0.449, or 4.49%.

10、Which of the following statements about a normal distribution is least likely accurate?

A)   The mean, median, and mode are equal.

B)   A normal distribution has excess kurtosis of three.

C)   The mean and variance completely define a normal distribution.

D)   Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.

The correct answer was B)    

Even though normal curves have different sizes, they all have identical shape characteristics. The kurtosis for all normal distributions is three; an excess kurtosis of three would indicate a leptokurtic distribution. The other choices are true.