1640 words  7 pages
Standard Deviation (1 of 3)
Introduction
So far, we have introduced two measures of spread; the range (covered by all the data) and the interquartile range (IQR), which looks at the range covered by the middle 50% of the distribution. We also noted that the IQR should be paired as a measure of spread with the median as a measure of center. We now move on to another measure of spread, the standard deviation, which quantifies the spread of a distribution in a completely different way.
Idea
The idea behind the standard deviation is to quantify the spread of a distribution by measuring how far the observations are from their mean, x. The standard deviation gives the average (or typical
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886 words  4 pages
Mean and standard deviation
The median is known as a measure of location; that is, it tells us where the data are. As stated in , we do not need to know all the exact values to calculate the median; if we made the smallest value even smaller or the largest value even larger, it would not change the value of the median. Thus the median does not use all the information in the data and so it can be shown to be less efficient than the mean or average, which does use all values of the data. To calculate the mean we add up the observed values and divide by the number of them. The total of the values obtained in Table 1.1 was 22.5 , which was divided by their number, 15, to give a mean of 1.5
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equal to ‘three fourths’ and X to ‘success’. Paste those three scatter plots below.

Calculating Descriptive Statistics
* Open the class survey results that were entered into the MINITAB worksheet.
2. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window. Type the mean and the standard deviation here.
Mean: 4.6Standard deviation: 1.429 
Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used
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Assignment #1: Virginia Capital Portfolio Optimization
Stock  Mean of Return  Standard Deviation 
IBM  1.27%  9.38% 
1) The below table shows the mean of IBM’s Stock to be 1.27% and the standard deviation to be 9.38%.
Stock  Mean  Standard Deviation 
Complete Portfolio of Weighted S&P, Lehman, and MSCI  0.67%  2.75% 
2)
The table above shows the mean and standard deviation of a portfolio with S&P 500, Lehman Brothers, and MSCI World Index when they are all equally weighted.
An argument that can be made for the client to sell IBM stock and diversify is about the risk involved. The standard deviation of IBM’s stock is sitting at about 9.34%, which is
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2911 words  12 pages
Product Risk And Uses Of Standard Deviation Finance Essay
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Product Risk And Uses Of Standard Deviation Finance Essay
Risks and returns are the two most important concepts in the investing world. The concept of return, which is the profit on investment, is a very clear subject to many investors but the risk is often vague. Several approaches had been
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SHOULDER FLEXION
Test Position * Subject supine * Flatten lumbar spine (flex knees) * Shoulder no abduction, adduction or rotation * (note: to measure glenohumeral motion, stabilize scapula)  Normal Range(for shoulder complex flexion) * 167o + or  4.7o (American Academy of Orthopaedic Surgeons) * 150o (American Medical Association) * 166o (mean), 4.7o (standard deviation), (Boone and Azen) 
Goniometer Alignment * Axis – center of humeral head near acromion process * Stationary arm – parallel midaxillary line * Moving arm – aligned with midline of humerus (lateral epicondyle)  Normal End Feel * Muscle Stretch 
SHOULDER EXTENSION
Test
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1643 words  7 pages

University of Phoenix Material
Week Two Practice Problems
Prepare a written response to the following questions.
Chapter 2
12. For the following scores, find the mean, median, sum of squared deviations, variance, and standard deviation:
1,112; 1,245; 1,361; 1,372; 1,472
Mean: 1,312.4
Median: 1,361
Sum of squared deviation: 76,089.2
Variance: 15,217.84
Standard deviation: 123.36
16. A psychologist interested in political behavior measured the square footage of the desks in the official office for four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures
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620 words  3 pages
1. For each company
A. Deterring the mean and standard deviation of the returns.
B. Calculate the coefficient of variation.
C. Determine which company appears to be more volatile with respect to its risk.
D. Identify the company with which you would choose to invest.
Part a:
Year  Company A Return  Company B Return  Average Market Return  Company A Deviation  Company A Deviation Squared  Company B Deviation  Company B Deviation Squared 
1985  5.0%  4.0%  2.0%  3.0%  0.1%  2.0%  0.0% 
1986  4.0%  8.0%  6.0%  2.0%  0.0%  14.0%  2.0% 
1987  3.0%  2.0%  7.0%  4.0%  0.2%  5.0%  0.3% 
1988  4.0%  5.0%  8.0%  4.0%  0.2
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computing variance of a portfolio.
Assumptions of Markowitz Model
• Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period. • Investors maximize one period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth. • Investors estimate the risk of the portfolio on the basis of the variability of expected returns.
Assumptions of Markowitz Model
• Investors base decision solely on expected return and risk, so that their utility curves are a function of expected return and the expected variance (or standard deviation) of returns only. • For a given level of risk
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1067 words  5 pages
1
Running head: UNIT 4 ASSIGNMENT 1
Fundamentals of Finance
BUS 3062
Rodtrice Johnson
3/7/16
Unit 4 Assignment 1
Dennis Hart
1. Q: Proficientlevel: "How do Cornett, Adair, and Nofsinger define risk in the M: Finance textbook and how is it measured?" (Cornett, Adair, & Nofsinger, 2016).
Distinguishedlevel: Describe the risk relationship between stocks, bonds, and Tbills, using the standard deviation of returns as the measure of risk.
Answer Proficientlevel: Risk is defined as the volatility of an asset’s returns over time. Specifically, the standard deviation of returns is used to measure risk. This computation measures the deviation from the
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546 words  3 pages
correlation between two stocks the greater the diversification benefit, the lower the risk of portfolio that combines them. When two stocks move more oppositely, their returns will tend to offset one another in most states, causing a return of a portfolio combining them to be less volatile.
2a)I collected 10 years of historical monthly data of Amazon and Yahoo stocks. From these adjusted closing prices, I calculated monthly returns and standard deviation of monthly returns for each stock. After I got my monthly returns and standard deviation I converted them to annual values by using formulas. Formulas that were given are below:
Annualized Mean Return= (1+Monthly Mean Return) ^121
Annualized
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679 words  3 pages
Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing 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 learn whether the process was
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1999 words  8 pages
Math 221
Quiz Review for Weeks 5 and 6
1. Find the area under the standard normal curve between z = 1.6 and z = 2.6.
2. A business wants to estimate the true mean annual income of its customers. It randomly samples 220 of its customers. The mean annual income was $61,400 with a standard deviation of $2,200. Find a 95% confidence interval for the true mean annual income of the business’ customers.
3. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual's IQ score is found to be 120. Find the zscore corresponding to this value.
4. Two high school students took equivalent language tests, one in German and one in French. The
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668 words  3 pages
University of Phoenix Material
Time to Practice – Week Two
Complete Parts A, B, and C below.
Part A
1. Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions?
2. For the following set of scores, fill in the cells. The mean is 74.13 and the standard deviation is 9.98.
Raw score Z score 
68.0 ? 
? –1.6 
82.0 ? 
? 1.8 
69.0 ? 
? –0.5 
85.0 ? 
? 1.7 
72.0
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1887 words  8 pages
MATH/GM 533 Final Exam
1. (TCO D) PuttingPeople2Work has a growing business placing outofwork MBAs. They claim they can place a client in a job in their field in less than 36 weeks. You are given the following data from a sample.
Sample size: 100
Population standard deviation: 5
Sample mean: 34.2
Formulate a hypothesis test to evaluate the claim. (Points : 10)
Ho: µ = 36; Ha: µ ≠ 36
Ho: µ ≥ 36; Ha: µ < 36
Ho: µ ≤ 34.2; Ha: µ > 34.2
Ho: µ > 36; Ha: µ ≤ 36
Ans. b.
H0 must always have equal sign, < 36 weeks
2. (TCO B) The Republican party is interested in studying the number of republicans that might vote in a particular
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643 words  3 pages
Three Hundred and EightyFive McDonald’s consumers were randomly selected and their ages measured. The age ranges were 15 and 65 years. Average consumer is aged 31 with a standard deviation of 14 years. Approximately half or more of their ages are above 31.
Income
The income of the randomly surveyed consumers is averaged at $30.82 and with a standard deviation of $14.04. Income range is $15 to $65 and there is enough evidence that half or more of these consumers averages $30.82 per year.
Strengths and Weaknesses of Team Members’ Individual Assignments
Efforts were made by each team member to better understand the use of the statistical tool made available to us (MegaStat). More
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699 words  3 pages
80. a. These cases are a population because that these cases account for each of the 25 tables that are filled on the night in question. b. Mean = (28 + 39 + 23 + 67 +37 + 28 +56 + 40 +28+50+ 51 + 45 + 44 + 65 + 61 + 27 + 24 + 61 + 34 + 44 + 64 + 25+ 24 + 27 + 29) / 25 = 40.84 Median = The median value is the same as the middle value, and this is the same as the 13th highest number = 39 c. The biggest value = 67, lowest value = 23; so, the range is 67 – 23 = 44 Standard deviation = sqrt([(28  40.84)^2 + (39  40.84)^2 + (...same pattern) + (29  40.84)^2] / 25 ) =14.55 82. a. Mean = (3 x 90 + 8 x 110 + 12 x 130 + 16 x 150 + 7 x 170 + 4 x 190) / 50 = 141.2 b. Standard deviation =sqrt((3(90
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Statistics in Business NAME:_________________________
Sections 4 and 5
Class 05 Assignment
Due Wed February 1, 2012
1. (EMBS problem 19, page 260) The average amount of precipitation in Dallas, Texas during April is 3.5 inches (The World Almanac, 2000). Assume that a normal distribution applies and that the standard deviation is 0.8 inches.
a. What percentage of Aprils do we expect precipitation to exceed 5 inches?
b. What percentage of Aprils do we expect less than 3 inches?
c. A month is classified as extremely wet if the amount of precipitation is in the upper 10% for that month. How much precipitation must there
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(return  Inflation)
U.S. Gov. TBills 3.50% 2.90% 0.60%
Lg.cap CS 12.10% 2.90% 9.20%
L.T. Corp. Bonds 6.20% 2.90% 3.30%
L.T. Gov. Bonds 5.60% 2.90% 2.70%
SmallCap. CS 14.60% 2.90% 11.70%
2. The following are the monthly rates of return for Nike and JNJ
Using an excel spreadsheet, compute the following:
a. Average monthly rate of return for each stock
b. Standard deviation of returns for each stock
c. Covariance between the rates of return
d. The correlation coefficient between the rates of return
Month Nike JNJ
1 5% 8%
2 3% 1%
3 6% 2%
4 9% 11%
5 2% 4%
6 3% 6%
Mean 33% 3%
Standard Deviation 5.72% 6.13%
Covariance 0.00146667
Correlation
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807 words  4 pages
HLT362V Week 1 Homework EX#16
Answers for EXERCISE 16 page 122 (Questions 1 4 are optional)• Mean and Standard Deviation
Exercise 16: Mean and Standard Deviation
1. The researchers analyzed the data they collected as though it were at what level of measurement?
a. Nominal
b. Ordinal
c. Interval/ratio
d. Experimental
Answer: c. The researchers analyzed the data as though it were at the interval/ratio level since they calculated means (the measure of central tendency that is appropriate only for interval/ratio level data) and standard deviations (the measure of dispersion for interval/ratio data) to describe their study variables.
2. What was the mean posttest empowerment
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891 words  4 pages
gender. Quantitative variables include subjects that are numerical and give us a clear visual as to what the subject looks like. For instance, if we see a qualitative variable such as cat, we only know that the variable is a cat. A quantitative variable could tell us the weight of the cat, giving us a visual to compare the different sizes of the different cats, i.e. cat one weighs ten pounds, cat two weighs fifteen pounds. In this situation, the descriptive statistics are relatively useless when calculating gender (the qualitative data). The mean, mode, standard deviation and count are important in the quantitative data analysis because these types of statistical information hold value
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1031 words  5 pages
Strayer University
MAT 300
Dr. Soosan Shahrokh
December 12, 2014
Bottling Company Case Study
In this project we were given the case of customer complaints that the bottles of the brand of soda produced in our company contained less than the advertised sixteen ounces of product. Our boss wants us to solve the problem at hand and has asked me to investigate. I have asked my employees to pull Thirty (30) bottles off the line at random from all the shifts at the bottling plant.
The next step in solving this problem is to calculate the mean (x bar), the median (mu), and the standard deviation (s) of the sample. All of those calculations were easily computed in excel. The mean was
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 0.004 
0.5  0.2873 
1  0.5031 
1.5  0.6427 
2  0.7519 
2.5  0.8247 
Figure 2: Absorbance readings of unknown Zinc concentration and their mean, standard deviation, and standard error of their mean
Unknkown Absorbances (ppm)  Mean unknown absorbance (ppm)  Standard Deviation  Standard Error of Mean 
0.7992  0.801567  0.002122  0.001225 
0.8033    
0.8022    
Figure 3: Absorbance with respect to concentration of zinc in ppm via external standardisation
Part B: Method of Standard Addition
Figure 4: Table of standard addition of unknown lead sample to 25ml of known lead standard, and absorbances
ml of known added  absorbance
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885 words  4 pages
A portfolios risk plays a huge role in an investors expected returns which is why it is so important to not only be able to measure this risk but also to have some sort of control over it. There are many different risk measures that are available which are becoming much easier to perform with the technology these days. Some of the most common include the standard deviation, Beta, Alpha and the sharp ratio. Using the correlation and covariance can also be useful when it come to diversifying a portfolio and reducing risk. Another thing that should be considered is the number of securities within the portfolio because this has a large impact on diversifiable risk.
1)Risk measures
Why
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282 words  2 pages
.Statistical Symbols and Definitions Matching Assignment
Match the letter of the definition on the right to the appropriate symbol on the left.
Symbols Definitions
1. S (Uppercase Sigma) B a. Null hypothesis
2. m (Mu) H b. Summation
3. s (Lowercase Sigma) E c. Factorial
4. p (Pi) I d. Nonparametric hypothesis test
5. e (Epsilon) G e. Population standard deviation
6. c2 (Chi Square) D f. Alternate hypothesis
7. ! C g. Maximum allowable error
8. H0 A h. Population mean
9. H1 F i. Probability
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1010 words  5 pages
evaluating a security at the time when one year Treasury bills were paying 3.45%. Calculate the following investment’s expected return and standard deviation. Should BJ, a riskaverse investor, invest in this security?
State Probability Return
1 0.15 6%
2 0.30 10%
3 0.40 12%
4 0.15 16%
2. The common stocks of companies A and B have the expected returns and standard deviations given below; the expected correlation coefficient between the two stocks is –0.35.
Expected Return Standard Deviation
Common Stock A 0.10 0.15
Common Stock B 0.06
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2018 words  9 pages
Statistics
Name
Institution
Question 1 of 20  5.0 Points 
When comparing two population means with an unknown standard deviation you use a t test and you use N2 degrees of freedom.
A. True 
B. False 

Reset Selection
Question 2 of 20  5.0 Points 
Pretend you want to determine whether the mean weekly sales of soup are the same when the soup is the featured item and when it is a normal item on the menu. When it is the featured item the sample mean is 66 and the population standard deviation is 3 with a sample size of 23. When it is a normal item the sample mean is 53 with a population standard deviation of 4 and a sample size of 7. Given this information we could
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on Yasmin’s stock over this ﬁveyear period?
b. What was the variance of Yasmin’s returns over this period? The standard deviation?
A. (1913+24+31+8)/5=69/5=13,8%
B. Variance=1/(51)*((0,1380,19)^2+(0,138+0,13)^2+(0,1380,24)^2+(0,1380,31)^2+(0,1380,08)^2)=0,02947
Standard deviation: square root of Variance: 0,1717=17,17%
4. Holding Period Return
A stock has had returns of 17.62 percent, 15.38 percent, 10.95 percent, 26.83 percent, and 5.31 percent over the past ﬁve years, respectively. What was the holding period return for the stock?
Holding period return= ((10,1762) *(1+0,1538) *(1+0,1095)*(1+0,2683)*(1+0,0531))1=40,85%
5. Risk Premiums
Refer to Table 10.1 in
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1281 words  6 pages
interval [3,7]?————[1] c. Compare µ to the value x you found in part a). ———————– ¯ Generate and store in column c2 1,000 values from exponential distribution with parameter λ = .125 as follows: random 1000 c2; exponential 8. Note: The mean µ and the standard deviation σ of such distribution are both equal to 1/λ = 8 and this is the value you are asked to enter in the command above. [3] d. Use desc command to ﬁnd the sample mean x and sample standard deviation s for ¯ these 1,000 data —————– and —————— Are x and s close to the value 1/λ = 8?———————– Why?——————————¯ [3] e. Print (and include in your assignment) the histogram of the 1,000 values you generated from this exponential distribution
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269 words  2 pages
tendency (mean, median or mode) do you think best describes the data set? Fully explain your answer.
Explain standard deviation
Explain what the standard deviation tells us about variation in our data.

**Remember to post substantial replies to at least two of your peers. You may find guidelines for acceptable response posts in the doc sharing portion of the course***
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771 words  4 pages
foreign currency rates. ROA was estimated with a random number
generation based on normally distributed amounts with a mean of 18% and a standard deviation
of 4% (see item (e) of Exhibit 8). The impact of fluctuations in foreign currency was estimated
based on the current rate of 1.514 $/Pound and a standard deviation of 0.17 (see instruction for
Part II, first bullet, item 3). We used a random number generator to determine the fluctuations
from year to year and then calculated the percentage change year over year. The percentage
fluctuation was applied to the calculated ROA to determine what the EBIT would be including
potential foreign currency fluctuations.
Taxes were estimated to
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4199 words  17 pages
BKM CHAPTER 7
1. Which of the following factors reflect pure market risk for a given corporation?
a. Increased shortterm interest rates
b. Fire in the corporate warehouse
c. Increased insurance costs
d. Death of the CEO, e. Increased labor costs)
(a) and (e) – The other three do not affect all participants in the economy.
2. When adding real estate to an asset allocation program that currently includes only stocks, bonds, and cash alternatives (riskfreemoney market investments), which of the properties of real estate returns affect portfolio risk? Explain.
a. Standard Deviation
b. Expected Return
c. Correlation with the returns of
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2310 words  10 pages
better than,” “is more
effective”
See left
text
H1
109
Conduct a test of hypothesis about a population mean.
Hypothesis Setups for
Testing a Mean ()
1010
Testing for a Population Mean with a
Known Population Standard Deviation — Example
Jamestown Steel Company
manufactures and assembles
desks and other office
equipment. The weekly
production of the Model A325
desk at the Fredonia Plant
follows the normal probability
distribution with a mean of 200
and a standard deviation of 16.
Recently, new production
methods have been introduced
and new employees hired. The
VP of manufacturing would like
to investigate whether there
has been a change in the
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1273 words  6 pages
cluster about the mean. The most common measure of variability is the variance. The variance is calculated by squaring and summing the deviation of the individual data points from the mean. The equation for variance is s²=Σ (X )²/(N 1). The square root of the variance provides the standard deviation of the sample, s. If you have your data in an Excel spreadsheet, you can easily calculate the mean and standard deviation by using the builtin functions, AVE and STDEV.
The sample mean and standard deviation are used to estimate the population mean and standard deviation, which are denoted by the Greek letters μ and σ. The mean of the population is the central tendency of the data. The equation for
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The following questions are taken from old practice exams found under PRACTICE EXAMS under ASSIGNMENTS. SOLUTIONS/ANSWERS TO THESE CAN BE FOUND UNDER PRACTICE EXAMS UNDER ASSIGNMENTS.
PRACTICE EXAM IIA 1 THRU 6, 8, 9, 14
1. The standard normal distribution has mean ______ and standard dev. ______.
2. Let z be a random variable with a standard normal distribution. Find P(2 < z < 1.2).
3. The life of a turntable is normally distributed with mean 2.3 years and std dev. .4 year. Find the probability that a turntable breaks down within 2 years. ( 4 decimal places)
4. For a random variable that is normally distributed, with mean 80 and standard deviation
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1989 words  8 pages
value computed from the standard deviation was 391.78 kg/m3 while the same computed from the resolution uncertainty was 24.402 kg/m3 In part 3, the time period of a pendulum was measured first using a stopwatch measured over various cycles and then an oscilloscope with help of a sensor. The mean time period calculated for 1, 6, 13, 25 cycles is 0.85s, 0.88s, 0.88s and 0.89s respectively. It was also observed that the relative error decreases with increase in number of cycles, i.e. relative error is minimized when averaging large number of single measurements than few readings over multiple cycles. The relative error in measuring over 1 cycle was 5.12% whereas for 25 cycles was 0.62%.
1
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854 words  4 pages
must consider the purchase of two stocks which would increase her market exposure heavily (around 80%). The two stocks are the California R.E.I.T. (Real Estate Investment Trust), which made equity and mortgage investments and Brown Group, Inc. which was a large manufacturer and retailer of shoes. First, she must calculate the variability of each stock. Variability is expressed through standard deviation. California R.E.I.T. produced an average return of 2.26% and had a standard deviation of 9.23%. Brown Group produced an average return of 0.67% and a standard deviation of 8.17%. Compared to the Vanguard fund, these are not good results for either individual stock. If Ms. Wolfe based
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1112 words  5 pages
.
It's a discrete random variable, because the values of the variable is one of the 6 values in the set {1,2,3,4,5,6}. Since this set is finite, the random variable is discrete. Also we only have a 1/6 chances when rolling a number. 
2. Calculate the mean and standard deviation of the probability distribution created by rolling a die. Either show work or explain how your answer was calculated.
Mean: 3.5 Standard deviation: 1.707Mean = 1(1/6)+2(1/6)+3(1/6)+4(1/6)+5(1/6)+6(1/6) = 3.5Standard Deviation= (13.5)^2(1/6)+(23.5)^2(1/6)+(33.5)^2(1/6)+(43.5)^2(1/6)+(53.5)^2(1/6)+(63.5)^2(1/6) = sqrt(2.196666…) = 1.7078 
3. Give the mean for the mean column of the Worksheet. Is
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856 words  4 pages
1 2.8%
36 1
We can note that histogram is bell shaped and symmetric. It agrees with the results predicted by the Central Limit Theorem which states that for “large” samples, the sampling distribution is approximately normal.
5. Standard deviation of the set of 36 sample means = 3.551804
Population standard deviation = 22.57
Sample standard deviation = = 3.57
Since both the values are very close so it agrees with the result predicted by the Central Limit Theorem.
Part 3. Finding z and tscores for Confidence Intervals
1. Using Excel, find the zscore that corresponds to the following Confidence Levels:
a. 80%
Answer: 1.282
b. 85%
Answer: 1.44
c
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929 words  4 pages
monthly returns for Vanguard S&P 500 Index Fund, R.J. Reynolds and Hasbro. Among those return data, the Vanguard has a maximum return of 34.46% and a minimum return of 10.14. The Reynolds has a maximum return of 112.49 and a minimum return of 31.48. The Hasbro has a maximum return of 71.03 and a minimum return of 15.36. The result turns out that the Reynolds has the highest average return as 1.87% with a highest standalone risk measured by the standard deviation which is 8.116, while the Vanguard has the lowest average return as 0.57% with a lowest standard deviation 3.602 which means the lowest standalone risk. The sum of the five years’ returns for Vanguard is 34.46%, 112.49% for
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549 words  3 pages
customers comes from suburban location at 30%, lastly 28% of the customers are from urban locations.
The 2nd individual variable is Size:
Below are the measures of central tendency, variation and other descriptive statistics. The calculations are displayed below:
Descriptive Statistics:
Size
Mean 3.42
Standard Error 0.24593014
Median 3
Mode 2
Standard Deviation 1.73898868
Sample Variance 3.02408163
Kurtosis 0.7228086
Skewness 0.52789598
Range 6
Minimum 1
Maximum 7
Sum 171
Count 50
Frequency Distribution:
Size Frequency
1 5
2 15
3 8
4 9
5 5
6 5
7 3
The mean household size of the customers is 3.42. The median of the data is 3 and the mode is 2. The standard
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2607 words  11 pages
= 9.1%
CV GH = 1.03.
[pic]S&P 50 = 16.4%.
CV S&P 50 = 1.10.
Standard deviation and coefficient of variation are measures of dispersion about the mean, and hence measure total risk. Total risk is the relevant measure of risk only for assets held in isolation.
Of the two total risk measures, coefficient of variation is the better one because it relates risk to the expected rate of return; that is, it standardizes the measure. (Note that a measure such as semivariance, which measures only downside risk, may be a better total risk measure than either standard deviation or coefficient of variation. However, if return distributions are approximately symmetric, then semivariance
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3853 words  16 pages
CHAPTER 7: OPTIMAL RISKY PORTFOLIOS
CHAPTER 7: OPTIMAL RISKY PORTFOLIOS
PROBLEM SETS 1. 2. (a) and (e). (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate. Portfolio variance now includes a variance term for real estate returns and a covariance term for real estate returns with returns for each of the other three asset classes. Therefore, portfolio risk is affected by the 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
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analyze the risks associated with each stock, a RiskFree rate of interest must be established in order to calculate the required rate of return for each stock. This information along with the stock’s beta, standard deviation, and variance will be measured on both a standalone basis and collectively in the portfolio.
RiskFree Rate of Return:
The RiskFree rate of Return represents the interest rate that would exist on a riskless security if no inflation were expected. One security considered to be a riskless security when analyzing stock data is the government Tbill. The logic behind considering this to be a riskless investment is because if necessary interest payments are not made
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10/24/2011
9
◦ Distribution of The Sample Mean
10
5
10/24/2011
Let X1, X2, . . . , Xn be a sequence of p y independent and identically distributed random variables each having mean μ and
variance σ2. Then for n large, the distribution of
X1 +・ ・ ・+Xn is approximately normal with mean nμ and
variance nσ2. i
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The Central Limit Theorem
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10/24/2011
Problem: An insurance company has 25,000 automobile policy holders If the yearly claim holders. of a policy holder is a random variable with mean 320 and standard deviation 540, approximate the probability that the total yearly claim exceeds 8.3 million.
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10/24/2011
Since the
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Compound Interest the situation in which interest paid on an investment during the first period is added
to the principal. During the second period, interest is earned on the original principal plus the interest
earned during the first period.
number of years
Annuity a series of equal dollar payments made for a specified
Annuity Due annuity in which the payments occur at the beginning of each period
Perpetuity an annuity with an infinite life
Amortized Loan a loan that is paid off in equal periodic payments
Risk potential variability in future cash flows
standard deviation a measure of risk when looking at stock in isolation
standard deviation measure of the dispersion of
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with Stock Return 
 Variance of Market Return 
β = Correlation Coefficient  × Standard Deviation of Stock Returns 
 Between Market and Stock  Standard Deviation of Market Returns 
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C.
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True.
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D. Answer is 0.13 * 0.13 * (0.5/100) = 0.0000845 and not B.
The Correlation Coefficient between the returns on two stocks can be calculated using the following equation:
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where
• ρ12 = the correlation coefficient between the returns on stocks 1 and 2,
• σ12 = the covariance between the returns on
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