burning0spear

Which of the following statements about a normal distribution is least accurate?

A) Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.

B) A normal distribution has excess kurtosis of three.

C) The mean and variance completely define a normal distribution.

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Even though normal curves have different sizes, they all have identical shape characteristics. The kurtosis for all normal distributions is three; an excess kurtosis of three would indicate a leptokurtic distribution. Both remaining choices are true.

burning0spear

An investor has the following assets:

• $5,000 in bonds with an expected return of 8%.
• $10,000 in equities with an expected return of 12%.
• $5,000 in real estate with an expected return of 10%.

What is the portfolio's expected return?

A) 10.00%.

B) 11.00%.

C) 10.50%.

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Expected return is the weighted average of the individual expected values. The expected return is: [(5,000) × (10.00) + (5,000) × (8.00) + (10,000) × (12.00)] / 20,000 = 10.50%.

burning0spear

A portfolio is equally invested in Stock A, with an expected return of 6%, and Stock B, with an expected return of 10%, and a risk-free asset with a return of 5%. The expected return on the portfolio is:

A) 7.0%.

B) 8.0%.

C) 7.4%.

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(0.333)(0.06) + (0.333)(0.10) + 0.333(0.05) = 0.07

burning0spear

Which of the following statements about the arithmetic mean is least accurate?

A) The arithmetic mean of a frequency distribution is equal to the sum of the class frequency times the midpoint of the frequency class all divided by the number of observations.

B) If the distribution is skewed to the left then the mean will be greater than the median.

C) The arithmetic mean is the only measure of central tendency where the sum of the deviations of each observation from the mean is always zero.

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If the distribution is skewed to the left, then the mean will be less than the median.

burning0spear

Which of the following statements about the median is least accurate? It is:

A) equal to the 50th percentile.

B) more affected by extreme values than the mean.

C) equal to the mode in a normal distribution.

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Median is less influenced by outliers since the median is computed as the “middle” observation. On the other hand, all of the data including outliers are used in computing the mean. Both remaining statements are true regarding the median.

burning0spear

What are the median and the third quintile of the following data points, respectively?

9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%

A) 13.1%; 13.6%.

B) 13.1%; 13.7%.

C) 12.8%; 13.6%.

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The median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7th term.
The formula for determining quantiles is: Ly = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8th and 9th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 − 0.136) = 0.1372, or 13.7%.

burning0spear

What does it mean to say that an observation is at the sixty-fifth percentile?

A) 65% of all the observations are below that observation.

B) 65% of all the observations are above that observation.

C) The observation falls within the 65th of 100 intervals.

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If the observation falls at the sixty-fifth percentile, 65% of all the observations fall below that observation.

burning0spear

Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:

A) 23%.

B) 21.5%.

C) 20.0%.

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The third quartile is calculated as: Ly = (7 + 1) (75/100) = 6. When we order the observations in ascending order: 7%, 10%, 12%, 15%, 20%, 23%, 27%, “23%” is the sixth observation from the left.

burning0spear

The following data points are observed returns.  

4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%, 28.1%

What return lies at the seventh decile (70% of returns lie below this return)?

A) 17.0%.

B) 18.4%.

C) 19.0%.

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The formula for the seventh decile is Ly = (n + 1)(7 / 10) = 7.70 or between the seventh and eighth return from the left. The seventh return is 17%, while the eighth return is 19%. Interpolating, we find that the seventh decile is 17% + 0.7(19% – 17%) = 18.4%.

burning0spear

When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful? The:

A) variance.

B) median.

C) standard deviation.

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The standard deviation is more useful than the variance because the standard deviation is in the same units as the mean. The median does not help in creating intervals around the mean.