manchester88

Which of the following statements regarding skewness is least accurate?

A) A distribution that is not symmetrical has skew not equal to zero.

B) A positively skewed distribution is characterized by many small losses and a few extreme gains.

C) In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean.

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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.

manchester88

A distribution with a mode of 10 and a range of 2 to 25 would most likely be:

A) positively skewed.

B) normally distributed.

C) negatively skewed.

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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.

manchester88

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

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

C) The distribution is positively skewed.

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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.

manchester88

If the historical mean return on an investment is 2.0% and the standard deviation is 8.8%, what is the coefficient of variation (CV)?

A) 1.76.

B) 6.80.

C) 4.40.

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The CV = the standard deviation of returns / mean return or 8.8% / 2.0% = 4.4.

manchester88

What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?

A) 40%.

B) 25%.

C) 20%.

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Coefficient of variation, CV = standard deviation / mean. The standard deviation is the square root of the variance, or 4½ = 2. So, CV = 2 / 10 = 20%.

manchester88

If stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:

A) 0.167.

B) 6.0.

C) 1.20.

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The coefficient of variation is the standard deviation divided by the mean: 5 / 30 = 0.167.

manchester88

The mean monthly return on a sample of small stocks is 4.56% with a standard deviation of 3.56%. What is the coefficient of variation?

A) 78%.

B) 128%.

C) 84%.

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The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean. 3.56 / 4.56 = 0.781, or 78%.

manchester88

An investor is considering two investments. Stock A has a mean annual return of 16% and a standard deviation of 14%. Stock B has a mean annual return of 20% and a standard deviation of 30%. Calculate the coefficient of variation (CV) of each stock and determine if Stock A has less dispersion or more dispersion relative to B. Stock A's CV is:

A) 1.14, and thus has more dispersion relative to the mean than Stock B.

B) 1.14, and thus has less dispersion relative to the mean than Stock B.

C) 0.875, and thus has less dispersion relative to the mean than Stock B.

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CV stock A = 0.14 / 0.16 = 0.875
CV stock B = 0.30 / 0.20 = 1.5
Stock A has less dispersion relative to the mean than Stock B.

manchester88

The mean monthly return on (U.S. Treasury bills) T-bills is 0.42% with a standard deviation of 0.25%. What is the coefficient of variation?

A) 60%.

B) 84%.

C) 168%.

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The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean, or 0.25 / 0.42 = 0.595, or 60%.

manchester88

Given a population of 200, 100, and 300, the coefficient of variation is closest to:

A) 30%.

B) 40%.

C) 100%.

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CV = (σ/mean)
mean = (200 + 100 + 300)/3 = 200
σ = √[(200 - 200)2 + (100 - 200)2 + (300 - 200)2 / 3] = √6666.67 = 81.65
(81.65/200) = 40.82%