| | | |Range |R |R | |Average Deviation |A.D. |A.D. | |Variance |δ2 |s2 | |Standard Deviation |Δ |s | |Others | |
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variance (or standard deviation) of real estate returns and the correlation between real estate returns and returns for each of the other asset classes. (Note that the correlation between real estate returns and returns for cash is most likely zero.) 3. (a) Answer (a) is valid because it provides the definition of the minimum variance portfolio. 4. The parameters of the opportunity set are: E(rS) = 20%‚ E(rB) = 12%‚ σS = 30%‚ σB = 15%‚ ρ = 0.10 From the standard deviations and the correlation
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x-bar = (157+132+109+145+125+139)/6=$134.5 s^2 = ((157-134.5)^2+(132-134.5)^2+(109-134.5)^2+(145-134.5)^2+(125-134.5)^2+(139-134.5)^2)/5 = $276.7 s=sqrt(s^2) = sqrt(276.7) =$ 16.634 b. 69.26% of the expense would fall within 1 standard deviation from the mean -> 134.5+/- 16.634 =
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Formulas: X < μ = 0.5 – Z X > μ = 0.5 + Z X = μ = 0.5 where‚ μ = mean σ = standard deviation X = normal random variable Normal Distribution Problems and Solutions – Example Problems: Example 1: If X is a normal random variable with mean and standard deviation calculate the probability of P(X<50). When mean μ = 41 and standard deviation = 6.5 Solution: Given Mean μ = 41 Standard deviation σ = 6.5 Using the formula Z = Given value for X = 50 Z = = = 1.38 Z = 1.38 Using
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standard deviation and the higher variance. If we compare both stocks‚ Reynolds is riskier than Hasbro in this case. The higher variance indicates higher chance that the actual return on Reynolds will deviate from the expected return. S&P 500 REYNOLDS HASBRO Mean/Average 0.574333 1.874833 1.183833 Variance 12.972333 87.730541 65.866763 Standard Deviation 3.601713 9.366458 8.115834 Answer 2. At individual stock level‚ Reynolds fluctuates more than Hasboro as it has higher Standard Deviation and
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processes. In one particular application‚ a client gave Quality Associates a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation for these data was .21; hence‚ with so much data‚ the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples‚ the client could quickly
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probability of over 99%; these plans are: CTC‚ HIC‚ and RCNC1. CTC costs are estimated to be the lowest when considering the average of $13.5m and standard deviation of only ~$2m which reflects a lower spread of the costs. Additionally‚ CTC cost savings average ~$14.5m when compared with the other plan offerings‚ with a low standard deviation which reflects more predictable savings. Similar results are obtained when we consider a safer accident rate (i.e.‚ 1 in 6‚6m flights). 2. Cost analysis
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STATISTICS - Lab #6 Statistical Concepts: Data Simulation Discrete Probability Distribution Confidence Intervals Calculations for a set of variables Open the class survey results that were entered into the MINITAB worksheet. We want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc > Row Statistics and select the radio-button corresponding to Mean. For Input variables:
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630 Standard Deviation- $2‚741‚746.033 Salaries with $100‚000 Bonus Data Mean- $2‚106‚742.122 Median- $1‚116‚630 Standard Deviation- $2‚741‚746.033 With the $100‚000 bonus‚ the mean and the median increased by $100‚000‚ because we increased all the salaries by $100‚000. However‚ the standard deviation was not affected‚ because the distribution of data was not affected. Salaries with 20% increase Data Mean- $2‚408‚090.547 Median- $1‚219‚956 Standard Deviation- $3‚290‚095.24
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between results‚ as initial values may have been different. Standard Deviation This measures the spread of data‚ and it can only be calculated when there is more than one repeat. The larger the standard deviation‚ the more widely spread the data is and therefore you have a less reliable mean. You can compare the standard deviation of two different sets of data‚ if the two standard deviation values
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