Quantitative Methods - 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:
- Option : B
- Explanation : 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:
- Option : A
- Explanation : Semivariance can be defined as the average squared deviations below the mean.
- Option : B
- Explanation : 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%.
- Option : B
- Explanation : 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
- Option : C
- Explanation : 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.
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