答案和详解如下： 1、A distribution with a mode of 10 and a range of 2 to 25 would most likely be: A) negatively skewed. B) normally distributed. C) positively skewed. D) a binomial distribution. The correct answer was 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. 2、If a distribution is skewed: A) each side of a return distribution is the mirror image of the other. B) the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean. C) it will be more or less peaked reflecting a greater or lesser concentration of returns around the mean. D) the distribution can be described completely by its mean and its variance. The correct answer was B) 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, and the ability to describe distribution completely by its mean and variance is a characteristic of a normal distribution. Peakedness of a distribution is measured by kurtosis. 3、Which of the following statements regarding skewness is FALSE? A) A positively skewed distribution is characterized by many small losses and a few extreme gains. B) A distribution that is not symmetrical has skew not equal to zero. C) A normal distribution will have a mean that is equal to its median. D) In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean. The correct answer was D) 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. 4、Which of the following statements about statistical concepts is FALSE? A) For a normal distribution, only 95% of the observations lie within ±3 standard deviations from the mean. B) The range of a set of data is found by taking the largest data value minus the smallest data value. C) The coefficient of variation is useful when comparing dispersion of data measured in different units or having large differences in their means. D) For any distribution, based on Chebyshev’s Inequality, 75% of the observations lie within ±2 standard deviations from the mean. The correct answer was A) For a normal distribution, 95% of the observations lie within plus or minus two standard deviations of the mean while 99% of the observations lie within plus or minus three standard deviations of the mean. All other statements are true. Note that 75% of observations for any distribution lie within plus or minus two standard deviations of the mean using Chebyshev’s inequality. | 
发表于 2008-4-8 18:20
| 
