manchester88

A distribution that has positive excess kurtosis is:

A) more skewed than a normal distribution.

B) less peaked than a normal distribution.

C) more peaked than a normal distribution.

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A distribution with positive excess kurtosis is one that is more peaked than a normal distribution.

manchester88

Which of the following statements about skewness and kurtosis is least accurate?

A) Positive values of kurtosis indicate a distribution that has fat tails.

B) Kurtosis is measured using deviations raised to the fourth power.

C) Values of relative skewness in excess of 0.5 in absolute value indicate large levels of skewness.

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Positive values of kurtosis do not indicate a distribution that has fat tails. Positive values of excess kurtosis (kurtosis > 3) indicate fat tails.

manchester88

In the most recent four years, an investment has produced annual returns of 4%, –1%, 6%, and 3%. The most appropriate estimate of the next year’s return, based on these historical returns, is the:

A) geometric mean.

B) harmonic mean.

C) arithmetic mean.

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Given a series of historical returns, the arithmetic mean is statistically the best estimator of the next year’s return. For estimating a compound return over more than one year, the geometric mean of the historical returns is the most appropriate estimator.

manchester88

If a distribution is positively skewed:

A) the mean is greater than the median.

B) the mode is greater than the median.

C) the mode is greater than the mean.

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For a positively skewed distribution, the mode is less than the median, which is less than the mean (the mean is greatest). Remember that investors are attracted to positive skewness because the mean return is greater than the median return.

manchester88

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.

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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.

manchester88

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) Point A represents the mode.

C) The mean value will be less than the mode.

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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%.

manchester88

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.

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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.

manchester88

If a distribution is positively skewed, then generally:

A) mean < median < mode.

B) mean > median < mode.

C) mean > median > mode.

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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.

manchester88

Twenty Level I CFA candidates in a study group took a practice exam and want to determine the distribution of their scores. When they grade their exams they discover that one of them skipped an ethics question and subsequently filled in the rest of his answers in the wrong places, leaving him with a much lower score than the rest of the group. If they include this candidate’s score, their distribution will most likely:

A) have a mode that is less than its median.

B) have a mean that is less than its median.

C) be positively skewed.

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With the low outlier included, the distribution will be negatively skewed. For a negatively skewed distribution, the mean is less than the median, which is less than the mode.

manchester88

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) Mode, mean, median.

C) Mean, median, mode.

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In a negatively skewed distribution, the mean is less than the median, which is less than the mode.