# Quantitative Methods - Quantitative Methods Section 2

>>>>>>>>Quantitative Methods Section 2

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

• 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.

• 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.