...Sports Another way of seeing it is to consider sports teams. In any set of categories, there will be teams that rate highly at some things and poorly at others. Chances are, the teams that lead in the standings will not show such disparity but will perform well in most categories. The lower the standard deviation of their ratings in each category, the more balanced and consistent they will tend to be. Teams with a higher standard deviation, however, will be more unpredictable. For example, a team that is consistently bad in most categories will have a low standard deviation. A team that is consistently good in most categories will also have a low standard deviation. However, a team with a high standard deviation might be the type of team that...
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...estimate of standard deviation, represented by s’, and compare its efficiency with the efficiency of other quick estimates of standard deviation, σ. Research Questions: This study questions whether the proposed calculation of s’ is an efficient quick method of estimating standard deviation, and how s’ compares to past quick estimates of standard deviation. Hypothesis: s’ can be used as a quick estimate of standard deviation by replacing the weighing of individuals by an estimated ranking of the individuals, with the weighing of groups of individuals. s’ is more efficient than other past quick estimates of standard deviation. Main Findings: Except for sample sizes less than 10, s’ is shown to have an insignificant difference when compared with s. There is only a slight increase in bias as the number of groups increases. The use of s’ as an estimate for standard deviation is efficient and is a preferable method of estimating standard deviation when it is more convenient to rank the individuals than to measure them. However, it is probable that in most cases ranking is more difficult than using the standard method of finding standard deviation. The method of calculating s’ used here is more efficient than past recorded estimates of standard deviation. The disadvantages of this method are error due to subjective ranking and the assumption of normality. Non-normality may affect the efficiency of s’. Mead, R. (1966). A quick method of estimating the standard deviation. Biometrika...
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...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. This familiar process is conveniently expressed by the following symbols: (pronounced "x bar") signifies the mean; x is each of the values of urinary lead; n is the number of these values; and σ , the Greek capital sigma (our "S") denotes "sum of". A major disadvantage of the mean is that it is sensitive to outlying points. For example, replacing 2.2 by 22 in Table 1.1 increases the mean to 2.82 , whereas the median will be unchanged. As well as measures of location we need measures of how variable the data are. We met two of these measures, the range and interquartile range, in Chapter 1. The range is an important measurement, for figures at the top and bottom of it denote the findings furthest removed from the generality. However, they do not give much indication of the spread of observations...
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...13. Variance and Standard Deviation (expected). Using the data from problem 13, calculate the variance and standard deviation of the three investments, stock, corporate bond, and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are correct, which investment would you choose considering both risk and return? Why? | |Forecasted Returns for Each Economy |Investment |Boom |Stable Growth |Stagnant |Recession |Stock |25% |12% |4% |-12% |Corporate bond |9% |7% |5% |3% |Government bond |8% |6% |4% |2% ANSWER Variance of Stock = 0.10 x (0.25 – 0.033)2 + 0.15 x (0.12 – 0.033)2 + 0.50 x (0.04 – 0.033)2 + 0.25 x (-0.12 – 0.033)2 = 0.10 x 0.0471 + 0.15 x 0.0076 + 0.50 x 0.0000 + 0.25 x 0.0234 = 0.0047 + 0.0011 + 0.0000 + 0.0059 = 0.0117 or 1.17% Standard Deviation of Stock = (0.0117)1/2 = 0.1083 or 10.83% Variance of Corp. Bond = 0.10 x (0.09 – 0.052)2 + 0.15 x (0.07 – 0.052)2 + 0.50 x (0.05 – 0.052)2 + 0.25 x (0.03...
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...Standard Deviation Abstract Paper Miguel Ramos, Waleska Molina, Pollyana Cotto, Jessica Casiano, QRB 501 Quantitative Reasoning for Business University Of Phoenix October 30, 2013 Prof. Angel Melendez-Melendez Standard Deviation Abstract Paper The purpose of this paper is to write a basic abstract for each article selected by the member of the learning team and establish for each article the purpose of the study, the research question(s), the hypothesis of the study, and the main findings of the study. The articles selected by each members of the learning team were: Explaining satisfaction in double deviation scenarios: the effects of anger and distributive justice (Jessica); Consumer Socialization in a Wired World: The Effects of Internet Use and Parental Communication on the Development of Skepticism to Advertising (Waleska); Real Estate in the Real World: Dealing with Non-Normality and Risk in an Asset Allocation Model (Pollyanna); and Social network productivity in the use of SNS. (Miguel). In the student (Jessica) article is an article in where the research has shown that more than half of attempted recovery efforts only reinforce dissatisfaction, producing a double deviation effect. Surprisingly, these double deviation effects have received little attention in service marketing literature. To fill this gap, this article aims to develop and empirically test a model of how customers form satisfaction judgments in double deviation scenarios. The article seeks...
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...QRB 501 WEEK 4 STANDARD DEVIATION A+ Graded Tutorial Available At: http://hwsoloutions.com/?product=qrb-501-week-4-standard-deviation Visit Our website: http://hwsoloutions.com/ Product Description PRODUCT DESCRIPTION QRB 501 week 4 Standard Deviation, Standard Deviation Introduction Standard deviations (SD) and variance are commonly used statistical tools that measure dispersion, risk, and predict certain outcomes in the business world through data. Through decades of academic research, investors and businesses have settled on standardized norms or patterns for various types of calculations, using standard deviations. Data sets, like mean or median, are manipulated to make an inference. This abstract will highlight five articles where the SD is assimilated in mixt conditions or settings. Each article will classify the purpose, any research questions, hypothesis, and the main findings. What to Use to Express the Variability of Data: Standard Deviation or Standard Error of Mean? Statistics is a major element in any industry, failing to provide adequate information to the reader can easily mislead the receivers. Therefore, using the correct highlights to display the variability of data, can minimize error and clarify any study. According to Barde (2012), “It is depressing to find how much good biological work is in danger of being wasted through incompetent and misleading analysis” (p. 113). Case in point, this experiment was based on the hypothesis that applying...
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...Standard deviation is key to predicting price volatility Wednesday, December 03 - 2008 at 12:10 Prices move up and down; all the time. Sometimes a little, but every now and then by large amounts. The measurement for these movements is called volatility, and is measured using standard deviation. Volatility is the most important price driver of option premiums. We are interested in future volatility. However, this is the only kind of volatility that we cannot know. We are able to calculate historical volatility, but is this a good bias for future volatility? Every option pricing model tries to evaluate options by ascribing probabilities to several different possible prices of the underlying value at expiry. Because the distribution of prices occurs in the future, and every underlying value has its own characteristics, there is no clear answer to the question of how probabilities must be allocated. But, as an approximation, most models (some with adjustments) start with the assumption of a normal distribution. A normal distribution curve is always defined by two things: the average or mean (reflected by the spike in the figure below) and the standard-deviation (the speed of expansion of the curve). The standard deviation can also be interpreted in terms of a probability of an occurrence. Once you know a certain mean and standard deviation, it is always possible to calculate the probability of an occurrence within a certain range of the mean. Usually you...
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...Abstract Hearing protectors are used in business to lessen the affects of noise exposure in construction, forestry, or other industrial settings. The purpose of this study was to analyze the relationship between attenuation performance and standard deviation. Businesses expect that hearing protectors provided to employees will reduce the noise level that they are exposed to, resulting in noise at an acceptable level. The hypothesis was that the attenuation performance of the hearing protector would fall within a reasonable range of values, or a norm. Research questions are whether or not various hearing protectors are reliable based on their attenuation performances, how reliability varies adversely with the mean attenuation and standard deviation, and the implications for the utilization of hearing protectors in the workplace. Test data indicated that attenuation performance varies based on the type of hearing protector used and the person using it; however, hearing protection devices should be designed so that the majority of people experience similar levels of attenuation. Results of the study also indicate that a large number of staff who use hearing protectors are actually protected more than necessary. Because of this they may be less likely to use the hearing protectors because they feel that they do not need them, especially in environments where they may experience lower noise levels. Exposure to high levels of workplace noise regularly can cause harm to employees’...
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...BUSINESS QUANTITATIVE TECHNIQUES. project NAME : JUNAID SHAFQAT SHARMEEN ARSHAD HASSAN ROLL NUM : 12133004 12133009 12133012 PROGRAM : MBA (BANKING & FINANCE) SUBMITTED TO : SIR ABID AWAN ABOUT THE AUTHORS 1st JUNAID SHAFQAT 12133004 3RD SEMESTER MBA (BANKING & FINANCE) 12133004@GIFT.EDU.PK 2ND SHARMEEN ARSHAD 12133009 3RD SEMESTER MBA(BANKING & FINANCE) 12133009@GIFT.EDU.PK 3RD HASSAN 12133012 3RD SEMESTER MBA(BANKING & FINANCE) 12133012@GIFT.EDU.PK Acknowledgement In the name of ALLHA ALMIGHITY the lord of the world who has bestowed us with abilities and blessed with knowledge so that we can make best of opportunities provide to us. First of all we are indebted toward ALLHA ALMIGHTY who has created us and made capable enough to with stand in the competitive world. If words could pay gratitude then we would like to pay our esteem gratitude to our most respected SIR ABID AWAN for assigning us this project of BUSINESS QUANTITATIVE TECHNIQUES. Throughout the course period he has been extremely cooperated with us and guided us at every single step he has been very encouraging and kind to us. At...
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...to return anything to the investor. However, investing in the stock market also presents the possibility for higher returns, the benefit of partial ownership in a company and the unlimited potential of a rising stock price, as well as the opportunity of further diversification of the portfolio. 3. The differences in return between stocks and bonds are that stocks have a higher return than bonds as shown with the average returns. Bonds have an average return ranging from about 3% to about 6% while stocks show an average return of about 13%. The risk in investments between stocks and bonds are shown in the standard deviation. While bonds have lower returns they also are less risky and less volatile than stocks. The volatility of bonds range from about 4% to about 9% while the volatility of stocks is about 20%. 4. Dow 30 Stock | Mean Return | Standard Deviation | ALUMINUM COMPANY AMER | 0.970588 | 6.721026 | ALLIED SIGNAL INC | 2.018627 | 6.450815 | AMERICAN EXPRESS CO | 1.831373 | 7.745903 | AT&T | 1.016667 | 6.36953 | BETHLEHEM STEEL CORP | 0.241176471 | 10.77440452 | BOEING CO | 1.16666667 | 6.62016621 | CHEVRON CORP | 1.332353 | 4.570247 | COCA COLA CO | 2.45 | 5.84709 | DU PONT | 1.732352941 | 6.147432238 | EASTMAN KODAK CO | 1.2627451 | 6.2074041 |...
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...Statistics is a powerful resource to determine important information. Statistics is used to determine whether the outcome of an experiment is the result of a relationship between specific factors or merely the result of chance. This concept is commonly used in the medical field to test drugs and vaccines and to determine causal factors of disease. Statistical also is used in the fields of psychology, environmental biology and other disciplines in which research is conducted through experimentation. Statistics are the mathematical calculations of numeric sets or populations that are manipulated to produce a probability of the occurrence of an event(Sullivan, 2003). A sample is used, and the results of the calculation are applied to an entire population. For example, it might be said that 80 percent of all adults in the United States drive a car. It would be difficult to ask each adult in the U.S. whether he or she drives a car, so a random number of people could be questioned, and the data could be statistically analyzed and generalized to apply to all adults in the U.S. This paper it shows three examples on how statistics relates to current life. Using the knowledge that I have obtained from this course, I will demonstrate techniques we have discussed in class to answer these questions. In 1798, Henry Cavendish measured the density of the earth using an instrument called a torsion balance. While the density is obviously not uniform, the value of the mean density is important...
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...Yinson Holding Berhad and YTL Power. While, the stock prices of 5 United State public listed company named by Adobe System INC, Alaska Air Group INC, Apple INC, The Aes Corporation and The NewYork Mellon Corporation. For stock prices of 5 United Kingdom public listed company named by Barclay, Bg Group, Big Yellow Group, Black Mount and Bovis Homes and lastly for the stock prices of 5 Indonesia public listed company named by Astra International, Bank Central Asia, Bank Danamon Indonesia, Kimia Farma and Unilever Indonesia. We also are required to demonstrate and explain the computations of annual return, risk, Sharpe ratio, return, covariance, beta, Treynor Ratio, portfolio standard deviation, and build a graph. THEORETICAL CONCEPTS In this assignment, we used the formula of Variances, Annual, Standard Deviation, Covariance, Correlation Coefficient, Beta, Variance Of Portfolio, Risk, Sharpe Ratio, Treynor Risk 1) Variance Variance measures how far a set of numbers is spread out. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. 2) Annual...
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...Chapter 1: Introduction – Defining the Role of Statistics in Business • Statistical Analysis: helps extract information from data and provides an indication of the quality of that information • Data mining: combines statistical methods with computer science & optimization in order to help businesses make the best use of the information contained in large data sets • Probability: helps you understand risky and random events and provides a way of evaluating the likelihood of various potential outcomes 1.1 - Why should you learn statistics? o Advertising. Effective? Which Commercial? Which markets? o Quality control. Defect rate? Cost? Are improvements working? o Finance. Risk – how high? How to control? At what cost. o Accounting. Audit to check financial statements. Is error material? o Other – economic forecasting, measuring and controlling productivity 1.2 – What is statistics? • Statistics: the art and science of collecting and understanding data o A complete and careful statistical analysis will summarize the general facts that apply to everyone and will also alert you to any exceptions. 1.3 – The Five Basic Activities of Statistics 1. Design Phase: will resolve these issues so that useful data will result a. Designing the Study involves planning the details of data gathering. Can avoid the costs & disappointment of find out – too late – that the data collected are not adequate to answer the important questions...
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...2. Descriptive Statistics Once the Data collection process has been completed the researcher must then try to make sense of the information collected. The data at this stage will be in its raw form and will generally not be suitable for presentation or interpretation The purpose of descriptive statistics, as the name suggests, is to describe a set of data. They are used to provide manageable summaries of data sets. They are the simplest and most widely used set of statistics and in many data analysis projects they will provide all the information required. There are many techniques available for describing a set of data. In this course we will look at three groups of univariate statistics, namely i) Frequency Distributions (ii) Measures of Central Tendency (iii) Measures of Dispersion We will also examine three bivariate techniques i) Crosstabs (ii) Tables of Means (iii) Correlation 2.1 Frequency Distributions - The frequency of a variable value is the number of times that value occurs in a set of data - A frequency distribution is simply a table of frequencies for all possible values of the variable. - They are relatively simple to construct and interpret; yet they still provide a very powerful tool for examining data. Example 2.1 2.1 Frequency Distribution of the number of cars owned by 500 households |Number of Cars |Frequency | |0 |70 ...
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...dividends may differ from what you expected. • Such future deviations from expectations represent, from today’s perspective, risk. • Standard deviation measures this risk (“average deviation from expectation”). Portfolios • When you form portfolios of securities, you combine the “expected returns” and “risks” of the individual securities in a particular way. • There are two ways to calculate the portfolio’s expected return and standard deviation from information about the individual securities. Method 1 STEP 1: Compute the return distribution of the portfolio. STEP 2: Then compute the expected value and the standard deviation of that distribution. Method 1 Example • Consider a “50-50” portfolio of two securities. • You are provided with the individual return distributions of the two securities: State Probability Return Security A Return Security B Portfolio Return 1 20% 50% 30% .5*50%+.5*30% 2 60% 0% 0% 0% 3 20% -50% -30% -.5*50%-.5*30% • STEP 1: Compute the portfolio return distribution. Method 1 Example State Probability Portfolio Return 1 20% 40% 2 60% 0% 3 20% -40% • STEP 2: Compute the expected value and standard deviation of the portfolio return distribution. – Expected portfolio return: 0% – Portfolio return variance: (.4-0)^2*20%+(0-0)^2*60%+(-.40)^2*20%=6.4% – Portfolio standard deviation: (.064)^(1/2)=29.3% (When squaring or taking the root...
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