答案和详解如下： Q2. If a distribution is positively skewed, then generally you could say: A) mean < median < mode. B) mean > median < mode. C) mean > median > mode. Correct answer is C) When a distribution is positively skewed the right side tail is longer than normal due to outliers. The mean will exceed the median, and the median will generally exceed the mode because large outliers falling to the far right side of the distribution can dramatically influence the mean. Q3. In a positively skewed distribution, the: A) median equals the mean. B) mean is greater than the median. C) mean is less than the median. Correct answer is B) In a right-skewed distribution, there are large positive outliers. These outliers increase the mean of the distribution but have little effect on the median. Therefore, the mean is greater than the median. Q4. In a negatively skewed distribution, what is the order (from lowest value to highest) for the distribution’s mode, mean, and median values? A) Median, mode, mean. B) Mean, median, mode. C) Mode, mean, median. Correct answer is B) In a negatively skewed distribution, the mean is less than the median, which is less than the mode. Q5. Consider the following graph of a distribution for the prices of various bottles of champagne. Which of the following statements regarding the distribution is least accurate? A) The distribution is negatively skewed. B) The mean value will be less than the mode. C) Point A represents the mode. Correct answer is C) The graph represents a negatively skewed distribution, and thus Point A represents the mean. By definition, mean < median < mode describes a negatively skewed distribution. Both remaining statements are true. Chebyshev’s Inequality states that for any set of observations (normally distributed or skewed), the proportion of observations that lie within k standard deviations of the mean is at least 1 – 1 / k2. Here, 1 – (1 / 1.32) = 1 − 0.59172 = 0.40828, or 40%. Q6. In a normal distribution, the:
A) mean is less than the mode. B) median equals the mode. C) mean is greater than the median. Correct answer is B) In a normal distribution, the mean, median, and mode are all equal. Q7. A distribution with a mean that is less than its median most likely: A) is negatively skewed. B) is positively skewed. C) has negative excess kurtosis. Correct answer is A) A distribution with a mean that is less than its median is a negatively skewed distribution. A negatively skewed distribution is characterized by many small gains and a few extreme losses. Note that kurtosis is a measure of the peakedness of a return distribution. | 
发表于 2009-1-8 17:53
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