How To Calculate the Variance and Standard Deviation

How To Calculate the Variance and Standard Deviation Variance and standard deviation are two closely related measures of variation that you will hear about a lot in studies, journals, or statistics class. They are two basic and fundamental concepts in statistics that must be understood in order to understand most other statistical concepts or procedures. Below, we’ll review what they are and how to find the variance and standard deviation. Key Takeaways: Variance and Standard Deviation The variance and standard deviation show us how much the scores in a distribution vary from the average.The standard deviation is the square root of the variance.For small data sets, the variance can be calculated by hand, but statistical programs can be used for larger data sets. Definition By definition, variance and standard deviation are both measures of variation for interval-ratio variables. They describe how much variation or diversity there is in a distribution. Both the variance and standard deviation increase or decrease based on how closely the scores cluster around the mean. Variance is defined as the average of the squared deviations from the mean. To calculate the variance, you first subtract the mean from each number and then square the results to find the squared differences. You then find the average of those squared differences. The result is the variance. The standard deviation is a measure of how spread out the numbers in a distribution are. It indicates how much, on average, each of the values in the distribution deviates from the mean, or center, of the distribution. It is calculated by taking the square root of the variance. A Conceptual Example The variance and standard deviation are important because they tell us things about the data set that we can’t learn just by looking at the mean, or average. As an example, imagine that you have three younger siblings: one sibling who is 13, and twins who are 10. In this case, the average age of your siblings would be 11. Now imagine that you have three siblings, ages 17, 12, and 4. In this case, the average age of your siblings would still be 11, but the variance and standard deviation would be larger. A Quantitative Example Let’s say we want to find the variance and standard deviation of the age among your group of 5 close friends. The ages of you and your friends are 25, 26, 27, 30, and 32. First, we must find the mean age: (25 26 27 30 32) / 5 28. Then, we need to calculate the differences from the mean for each of the 5 friends. 25 – 28 -326 – 28 -227 – 28 -130 – 28 232 – 28 4 Next, to calculate the variance, we take each difference from the mean, square it, then average the result. Variance ( (-3)2 (-2)2 (-1)2 22 42)/ 5 (9 4 1 4 16 ) / 5 6.8 So, the variance is 6.8. And the standard deviation is the square root of the variance, which is 2.61. What this means is that, on average, you and your friends are 2.61 years apart in age. Although it’s possible to calculate the variance by hand for smaller data sets such as this one, statistical software programs can also be used to calculate the variance and standard deviation. Sample Versus Population When conducting statistical tests, it’s important to be aware of the difference between a population and a sample. To calculate the standard deviation (or variance) of a population, you would need to collect measurements for everyone in the group you’re studying; for a sample, you would only collect measurements from a subset of the population. In the example above, we assumed that the group of five friends was a population; if we had treated it as a sample instead, calculating the sample standard deviation and sample variance would be slightly different (instead of dividing by the sample size to find the variance, we would have first subtracted one from the sample size and then divided by this smaller number). Importance of the Variance and Standard Deviation The variance and standard deviation are important in statistics, because they serve as the basis for other types of statistical calculations. For example, the standard deviation is necessary for converting test scores into Z-scores. The variance and standard deviation also play an important role when conducting statistical tests such as t-tests. References Frankfort-Nachmias, C. Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.

Commodum Essay Example | Topics and Well Written Essays - 6750 words

Commodum - Essay Example In 2008 Blair Connolly, Inc. was issued U.S. Patent Number 7,413,250 for the utility of a back support design. â€Å"Commodum† Latin for â€Å"comfort† is the first ergonomic office chair created that utilizes the patented back support design. The patent gives the company a competitive advantage over competitors because they have a novel design that cannot be imitated in the United States. The product will be strategically positioned as a high-end ergonomic office chair and promotional methods will highlight emotional benefits including: comfort, relaxation, vitality, status, and luxury. Commodum will be introduced using a skimming pricing strategy and consumers’ will most likely consider the product a high involvement purchase. Direct marketing will highlight important attributes such as service, quality and warrantee to help reduce cognitive dissonance often associated with high-involvement purchases. The ergonomic furniture giants in the U.S. primary consist o f two companies Herman Miller and Steelcase and have the two best ergonomic chairs on the market. The Herman Miller â€Å"Aeron† is considered the â€Å"gold standard† in ergonomic seating, which everything else is compared to it. The Steelcase â€Å"Leap† is more luxurious than the Aeron and has a slightly higher price. These companies have targeted the business office furniture segment and have been very successful. It would be more difficult for Commodum to penetrate the business office furniture market and would be impossible to compete in terms of price. Also, with the current economic environment businesses will be less likely to make major purchases on a new product that do not have a brand reputation established. However, home furnishings consumers are less aware of brand name and are a better market segment for Commodum to target. More specifically, Generation Xers and Baby-boomers are the best target market for the company because they spend more on ho me furnishings than any other generations. Baby-boomers and Xers are more likely to have discretionary income and home furniture purchases have been found to be discretionary in nature. Throughout history, there has been a correlation between furniture purchases and life stages, including: getting married, buying a house, children moving out and retiring. Baby Boomers and Generation Xers are experiencing life a stage associated with home furnishings consumption and makes them a powerful target market for Commodum. Additionally, recent socio-economic trends have created a growing home office furniture market and many Baby Boomers will be working longer than expected and will be using home offices more frequently. Technological advancements have led to a â€Å"hiving trend† and consumers are using their home as hub for communication. In conclusion, there is great opportunity for Commodum to succeed in the growing home office furniture Market, but will not be without barriers. H erman Miller and Steelcase may focus more promotional efforts on the home furniture consumer and may be hard to compete with. However, the novelty of the patented design makes the product unique and is the key component to strategy. With strategic positioning and promotion efforts San Diego should be a good market to launch Commodum. Historically, the housing market has been a market driver for home furnishing consumption and if the company can time the launch of Commodum with the housing market recovery it could lead to a lucrative business opportunity. 2. Table of Contents 1. Executive Summary†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦1 2. Table of Contents†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦3 3. Introduction†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦5 3.1 Background of the Problem†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦

Case study of Cherie Cosmestics Ltd Elegante Division

Of Cherie Cosmestics Ltd Elegante Division - Case Study Example or a company’s top level management to put into place reliable systems that can effective coordinate communication process and other important aspects of management. The communication function of effective management is responsible for creating reliable communication channels as well as structures that can be followed by all company workers. It is important to understand that all branch managers in a large company work towards a similar goal, that of success and increase of market share, for this reason, there is a need for collaboration and consultations among the managers. However, it is important that all these consultations and collaborations have to follow certain laid down procedures to avoid conflict of interest and the need to outdo each other at the expense of company goals and objectives and the spirit of good governance. Communication is an important function of any business activity, it ensures that directives are set effectively and implemented by company workers (Kuhn 2005). Effective communication has been the chief cornerstone of any development in any organisation; in fact, it is what enables company and organizational managers to carry out their basic functions and duties in the organisation. Communication skills, whether formal or informal have always been cited as the basis for the success of any business activity (Cheney 2007). Systems that do not have poor communication mechanisms often end up having misplaced priorities with people doing what they feel is pleasant to them and not what is stipulated in the company’s effective practice. The problems affecting the management function at Cherie Cosmetics Limited can be traced down to a breakdown in the communication process. In the first place, the company’s vice president has not taken steps to address the challenges and bring about sound management systems and communication in the company. There appears that some managers like Heather have the passion of working in this company and

Angles and Demons by Dan Brown Essay Example for Free

Angles and Demons by Dan Brown Essay Angles and Demons by Dan Brown was a reading choice out of curiosity rather than real interest because of the Da Vinci Code by the same author. I wanted to see what other works of fiction Dan Brown came up with before his controversial book. This book had me raising my eyebrows more than a few times with story line but that did not stop me from turning the pages until I got to the end. Angels and Demons basically follows the same formula as the Da Vinci Code. It begins with a murder which only Robert Langdon seems capable of solving with his knowledge of religious iconology and history; a strong female character, Vittoria Vetra, daughter to the murder victim Leonardo Vetra, assists Langdon in his â€Å"quest†; a hired assassin who is delusional, a fanatic and has unquestionable loyalty to his belief carries out an unforeseen but well-crafted plan; an ancient secret society, the Illuminati, is out to get revenge on the Church; finally, an unexpected mastermind who calls himself as Janus, works behind the curtains. An anti-matter canister was stolen from CERN when Leonardo Vetra was murdered and this is assumed to have a life span of 24 hours before the batteries die and it explodes. Brown remains true to using archaic bits of knowledge to leave a trail for Robert Langdon and Vittoria Vetra to follow from Switzerland to the Vatican City in order to find the missing anti-matter canister and find the murderer of Leonardo Vetra. The plot thickens when the anti-matter canister bomb threatens the Vatican and the conclave in the process of choosing the new Pope. The book ends dramatically with a seemingly miraculous event followed by the declaration of a new Pope. Though I enjoyed the chase more from Angels and Demons rather than the Da Vinci Code, I must say that, as a priest, Brown seems have some issues with the Church to come up with troubling concepts for his books. First you have Leonardo Vetra, a priest who turns away from the Church. He becomes a leading physicist of CERN and, together with his adopted daughter, tries to find God through science and research. They seem to be successful with the development of the anti-matter, which was stolen when Vetra was murdered. You also have a Pope who sired a child with a nun, though through artificial means. The child later becomes his camerlengo, the Pope’s Chamberlain. The camerlengo, Carlo Ventresca, unaware of his paternal parentage, murders the Pope upon knowing his dark secret with the belief that he is both cleansing and protecting the Church. Though the book is admittedly a work of fiction, it borders on tarnishing how Catholics and non-Catholics may view the Church and its priests. Brown puts into question the honesty and loyalty of priests to the Mother Church and their commitment to the vow of celibacy, as seen with the Pope. It is appalling to think that Jesus’ surrogates on Earth would be the first ones to violate their vows. Brown also pits religion versus science. Leonardo Ventra is murdered for his research on anti-matter which can supposedly prove the beginning of life, that science can prove God’s existence. I’d like to think that religion is a matter of faith and science is a matter of fact, the two just can’t mix when it comes to explaining God. Then you have the camerlengo who is himself delusional and a fanatic in his belief that the Church, and not science, is the saving power of the world with himself at the wheel of salvation. He goes to great lengths to get the world’s attention, discredit Science and put the Church on a pedestal for the world to see. Angels and Demons made me uncomfortable with the image of the Church that it created – a divided, secretive, vindictive and vulnerable body. Readers, both Catholics and non-Catholics should be discriminating of the events in this book, lest they forget that this is only a work of fiction.

Educating Rita :: English Literature

Educating Rita Willy Russell’s play â€Å"Educating Rita† only uses one main setting and two main characters. Some people may think that these would make the play seem boring. Russell actually makes the play quite interesting and entertaining by using dramatic devices such as the whiskey bottle and the telephone call. He does this to give us as much information as possible about the characters and their personalities. The play, which is set in the early 1980s, deals with the clashes between education and culture. It is about a middle-aged university lecturer called Frank. He is currently in a relationship with Julia. This relationship is not going too well as Frank is an alcoholic and would much rather go to the pub than go home to Julia. There is also Rita a 26-year-old woman who didn’t have a good education when she left school due to her parents’ working class background. She is now keen and eager to learn even though her husband Denny thinks that it is time for her to settle down and have children. Rita has set her sights higher than this. Rita is currently working as a hairdresser, but wants to achieve so much more than that, she wants an education. We get an idea of what sort of personality Frank has got by the conversation he has with Julia when she calls him to see when he was coming home. Although Frank had other Ideas, he was planning on going to the pub. We could see this by, â€Å" Yes I shall go to the pub† and â€Å"I don’t need determination to get me to the pub†. We get the impression that Frank does not care a great deal about Julia although it’s clear she loves him. When Frank was told that he was going to be tutoring Rita who is an open university student he was not very happy, the only reason he had took the job was so that he could make more money to spend on alcohol. Frank guessed that she was going to be â€Å"some silly woman†. This gives us the impression that Frank likes to use stereotypes and thinks that there is not much point. He soon realises that Rita has quite a lot to offer in regard to he uniqueness. The Playwright Russell wants to show how class affects education. When we first meet Rita we see that she is not the normal student Frank was expecting. She swears and uses informal colloquial language. This makes us think that Rita is not at all nervous about starting Open University and also makes her working class background obvious.

Is Chivalry Dead

Is Chivalry Dead?! What do you think of when you hear the word â€Å"chivalry†? I can’t speak for everyone but I know most of us, when we hear or think about the word â€Å"chivalry,† automatically we picture images of such figures as the legendary King Arthur and his Knights of the Round Table, Prince Charming, Gawain and The Green Knight, castles, and images of heavily armor knights saving princess or the cliche-ic â€Å"damsels in distress†. Though myths and fairytales illustrate this picture of chivalry, this in fact is a result of what the world has come to mean.Originally, the word â€Å"chivalry† had a different meaning. During the middle ages, the individuals who lived during this time use chivalry as a â€Å"code of conduct†. This â€Å"code of conduct† was put in place help the society become better by organizing it. People who lived during the Middle Ages supported the â€Å"code of conduct† because they felt it may h elp control the nation and help it gain more power. With any society, if chaos arises something is put into place for it to be demolished.For example, laws are created to provide a society with some type of order. Therefore, chivalry was created to control a society. â€Å"Chivalry wasn’t only to regulate the disorganization within a society but it also provided individuals at the type of the social ladder to be viewed with high esteem, particularly knight†. In order for a knight to make a name for himself or be recognized as honorable, he had to follow the behavioral code of chivalry.In modern society, one might speculate if chivalry has influence other people from across the globe. Although it pretty safe to say that in our society, chivalry has not fully impact us as a society, neither socially or culturally. Therefore providing truth to the saying that chivalry is dead. In medieval times, power in Europe was dispersed to the people of hierarchy. The people of great nobility, such as the king, had control of people who were viewed as inferior, such as the peasants.The earliest way for the nobles to protect themselves and land is through feudalism. Feudalism is a social system based on a hierarchy which consists of social, political, and economic systems. The purpose of the feudalism system was to give the nobles a chance to have power over lands and people. â€Å"This control would be so successful that it would provide a way for the king to give knights things such as gold or land in exchange for their loyalty and service to the kingdom†. This was the bases for the â€Å"code of conduct. †

Aristotle s Views On Morality And Happiness - 1948 Words

Jared Sanders 5/4/16 PHI 372: Ethical Inquiry Term Paper What, if anything, does happiness have to do with morality. According to Aristotle’s Nicomachean Ethics, there is a direct connection between morality and happiness. Aristotle states that happiness is the main goal of human existence. He follows this idea by saying the only way to achieve happiness is through his account of morality. Aristotle’s â€Å"happiness† is a translation of the Greek word Eudaimonia. A definition of Eudaimonia could be â€Å"the highest human good† or â€Å"well-being†, but it is not simply a word with a definition but a concept that needs to be broken down and understood. In connection with happiness is morality. According to Aristotle, only certain actions have genuine moral worth, which is heavily based upon reason. To live a moral life and achieve happiness one must achieve human excellence through moral and intellectual virtue. To make the connection between morality and happiness, we must understand these concepts in accordance with Aristotle. Aristotle’s concept of happiness stems from his search to find the â€Å"Highest Good† for man. His process starts with the idea of ends. An end is a good at which all things aim. An end can be considered to be an end â€Å"goal†. He makes the point that there is a cycle where you aim for an end which will help you achieve another end, which will help you achieve another end. An example of this is going to college. You study hard in high school to achieve the end ofShow MoreRelatedAristotle And Aristotle s Theory Of Moral Virtue1229 Words   |  5 PagesNietzsche and Aristotle were two of the most significant philosopher of not only their time but their works has lasted throughout the centuries to influence even some today’s greatest minds. 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According to Hume, the judgments and recommendations of morality arise not from reason, but from moral sense. Hume argued that virtue is always accompanied by a feeling of pleasure, and vice by a feeling of pain. Therefore, we praise an instance of virtuous action precisely because it stimulates in us a pleasing feeling, and we avoid committing a vicious action because we anticipate that doing soRead More Ethical and Philosophical Questions about Value and Obligation977 Words   |  4 Pageshow can we view the philosophical ethics of Mill, Kant, Aristotle, Nietzsche, and the ethics of care? III For Mill, the question is what is the relation between his (metaethical) empirical naturalism and his (normative) qualitatively hedonist value theory and his utilitarian moral theory? One place we can see Mill?s empiricism is his treatment, in Chapter III, of the question of why the principle of utility is ?binding?, how it can generate a moral obligation. 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