Quantitative Methods MCQ - Quantitative Methods Section 2

1 The return on equity for four hypothetical companies from a list of 100 companies is given below:

Little Wonder	10.5%
Genesis Ltd.	16.25%
Moral Corp.	9.81%
Travis Ltd.	12.0%

The sample standard deviation is closest to:

Use the following keystrokes to calculate the sample standard deviation: [2nd] [DATA] [2nd] [CLR WRK] X01 = 10.5 X02 = 16.25 X03 = 9.81 X04 = 12 s represents the value of sample standard deviation = 2.88.

2 Semivariance is defined as the average squared deviation:

Semivariance can be defined as the average squared deviations below the mean.

3 According to Chebyshev’s inequality, in a population of 1000 what is the minimum proportion of observation that must lie within three standard deviations of the mean, regardless of the shape of the distribution?

Chebyshev's inequality holds for any distribution, regardless of shape, and states that the minimum proportion of observations located within k standard deviations of the mean is equal to 1– 1/k2. In this case, k = 3 and 1– 1/9 = 0.89 or 89%.

4 A sample of 320 observations is randomly selected from a population. The mean of the sample is 144 and the standard deviation is 12. Based on Chebyshev’s inequality, the endpoints of the interval that must contain at least 75% of the observations are closest to:

According to Chebyshev‟s inequality, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1– 1/k2 for all k > 1. For k = 2, that proportion is 1– 1/22, which is 75%. The lower endpoint is, therefore the mean (144) minus 2 times 12 (the standard deviation) and the upper endpoint is 144 plus 2 times 12. 144– (2 × 12) = 120; 144 + 2(12) = 168

5 According to Chebyshev’s inequality, at least 88.89 percent of the observations for any distribution must lie within:

The formula for Chebyshev‟s inequality is: 1 – 1/k2 = % of distribution 1 – 1/k2 = 0.8889; solving for k, we get k = 3 88.89% of any distribution lies within 3 standard deviations.

Company	Expected Return	Standard Deviation
Gala Cement	10%	8%
Aqua Fertilizer	17%	20%