1215

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.

1215

If a distribution is positively skewed:

A) the mode is greater than the median.

B) the mean 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.

1215

In a positively skewed distribution, what is the order (from lowest value to highest) for the distribution’s mode, mean, and median values?

A) Mean, median, mode.

B) Mode, mean, median.

C) Mode, median, mean.

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

1215

Consider the following graph of a distribution for the prices for various bottles of California-produced wine.

Which of the following statements about this distribution is least accurate?

A) The graph could be of the sample $16, $12, $15, $12, $17, $30 (ignore graph scale).

B) The distribution is positively skewed.

C) Approximately 68% of observations fall within one standard deviation of the mean.

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This statement is true for the normal distribution. The above distribution is positively skewed. Note: for those tempted to use Chebyshev’s inequality to determine the percentage of observations falling within one standard deviation of the mean, the formula is valid only for k > 1.

The other statements are true. When we order the six prices from least to greatest: $12, $12, $15, $16, $17, $30, we observe that the mode (most frequently occurring price) is $12, the median (middle observation) is $15.50 [(15 + 16)/2], and the mean is $17 (sum of all prices divided by number in the sample). Time-Saving Note: Just by ordering the distribution, we can see that it is positively skewed (there are large, positive outliers). By definition, mode < median < mean describes a positively skewed distribution.