Q1. A distribution with a mode of 10 and a range of 2 to 25 would most likely be:

A)   normally distributed.

B)   positively skewed.

C)   negatively skewed.

Q2. Which of the following statements about statistical concepts is least accurate?

A)   The coefficient of variation is useful when comparing dispersion of data measured in different units or having large differences in their means.

B)   For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean.

C)   For any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean.

Q3. Which of the following statements regarding skewness is least accurate?

A)   In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.

B)   A distribution that is not symmetrical has skew not equal to zero.

C)   A positively skewed distribution is characterized by many small losses and a few extreme gains.

Q4. If a distribution is skewed:

A)     the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.

B)     it will be more or less peaked reflecting a greater or lesser concentration of returns around the mean.

C)     each side of a return distribution is the mirror image of the other.

答案和详解如下：

Q1. A distribution with a mode of 10 and a range of 2 to 25 would most likely be:

A)   normally distributed.

B)   positively skewed.

C)   negatively skewed.

Correct answer is B)

The distance to the left from the mode to the beginning of the range is 8. The distance to the right from the mode to the end of the range is 15. Therefore, the distribution is skewed to the right, which means that it is positively skewed.

Q2. Which of the following statements about statistical concepts is least accurate?

A)   The coefficient of variation is useful when comparing dispersion of data measured in different units or having large differences in their means.

B)   For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean.

C)   For any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean.

Correct answer is B)

For a normal distribution, 95% of the observations lie within ±2 standard deviations of the mean while 99% of the observations lie within plus or minus three standard deviations of the mean. Both remaining statements are true. Note that 75% of observations for any distribution lie within ±2 standard deviations of the mean using Chebyshev’s inequality.

Q3. Which of the following statements regarding skewness is least accurate?

A)   In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.

B)   A distribution that is not symmetrical has skew not equal to zero.

C)   A positively skewed distribution is characterized by many small losses and a few extreme gains.

Correct answer is A)

For a normal distribution, the mean will be equal to its median and 95% of all observations will fall within plus or minus two standard deviations of the mean. For a skewed distribution, because it is not symmetrical, this may not be the case. Chebyshev’s inequality tells us that at least 75% of observations will lie within plus or minus two standard deviations from the mean.

Q4. If a distribution is skewed:

A)     the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.

B)     it will be more or less peaked reflecting a greater or lesser concentration of returns around the mean.

C)     each side of a return distribution is the mirror image of the other.

Correct answer is A)

Skewness is caused by the magnitude of positive deviations from the mean being either larger or smaller than the magnitude of negative deviations from the mean. Each side of a skewed distribution is not a mirror image of the other. Peakedness of a distribution is measured by kurtosis.

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