When the Standard Deviation Is Equal to Zero

The sample standard deviation is a descriptive statistic that measures the spread of a quantitative data set. This number can be any non-negative real number. Since zero is a nonnegative real number, it seems worthwhile to ask, â€Å"When will the sample standard deviation be equal to zero?† This occurs in the very special and highly unusual case when all of our data values are exactly the same. We will explore the reasons why. Description of the Standard Deviation Two important questions that we typically want to answer about a data set include: What is the center of the dataset?How spread out is the set of data? There are different measurements, called descriptive statistics that answer these questions. For example, the center of the data, also known as the average, can be described in terms of the mean, median or mode. Other statistics, which are less well-known, can be used such as the midhinge or the trimean. For the spread of our data, we could use the range, the interquartile range or the standard deviation. The standard deviation is paired with the mean to quantify the spread of our data. We can then use this number to compare multiple data sets. The greater our standard deviation is, then the greater the spread is. Intuition So let’s consider from this description what it would mean to have a standard deviation of zero. This would indicate that there is no spread at all in our data set. All of the individual data values would be clumped together at a single value. Since there would only be one value that our data could have, this value would constitute the mean of our sample. In this situation, when all of our data values are the same, there would be no variation whatsoever. Intuitively it makes sense that the standard deviation of such a data set would be zero. Mathematical Proof The sample standard deviation is defined by a formula. So any statement such as the one above should be proved by using this formula. We begin with a data set that fits the description above: all values are identical, and there are n values equal to x. We calculate the mean of this data set and see that it is   x (x x . . . x)/n nx/n x. Now when we calculate the individual deviations from the mean, we see that all of these deviations are zero. Consequently, the variance and also the standard deviation are both equal to zero too. Necessary and Sufficient We see that if the data set displays no variation, then its standard deviation is zero. We may ask if the converse of this statement is also true. To see if it is, we will use the formula for standard deviation again. This time, however, we will set the standard deviation equal to zero. We will make no assumptions about our data set, but will see what setting s 0 implies Suppose that the standard deviation of a data set is equal to zero. This would imply that the sample variance s2 is also equal to zero. The result is the equation: 0 (1/(n - 1)) ∑ (xi - x )2 We multiply both sides of the equation by n - 1 and see that the sum of the squared deviations is equal to zero. Since we are working with real numbers, the only way for this to occur is for every one of the squared deviations to be equal to zero. This means that for every i, the term (xi - x )2 0. We now take the square root of the above equation and see that every deviation from the mean must be equal to zero. Since for all i, xi - x 0 This means that every data value is equal to the mean. This result along with the one above allows us to say that the sample standard deviation of a data set is zero if and only if all of its values are identical.

Analyse the Argument of the Existence of God from...

i) Analyse the Argument for the Existence of God from Religious Experience (18) The argument for the existence of God from Religious Experience is a simple one, with only two premises. The first being that some people have, or have had a religious experience, the second premise is that these are only explicable though God, thus leading to the conclusion that God exists. This leads us to question, what exactly are religious experiences? Theologians have struggled for centuries trying to define what a religious experience is, with many believing a religious experience to be a sort of revelation, meaning that God reveals some part of hi nature to the experient. St Thomas Aquinas believed that to be his Revealed Theology, where truths†¦show more content†¦Swinburnes third type is a strong feeling, a conviction that they were experiencing, even though there is no phenomena surrounding the experience. The penultimate type is witnessing a perfectly normal experience, such as the Grand Canyon, which creates a numinous experience. The final type of experience is in perceiving a very unusual public object, like a miracle, for instance, the resurrection. To help identify a religious experience, William James put forward four characteristics of a typical experience. The first being passivity: how in control the experient is; as whilst you undergo a religious experience, you take on an alternative personality outside of your own, surrendering your own control to God. The second quality is ineffability, where the experient cant quite put the occurrence into words. Another characteristic of a religious experience is the Noetic Quality of said experience. This quality is the knowledge that is gained in a religious experience, knowledge that cannot be gained in a conventional manner, and tells you something that you otherwise wouldnt know. The final quality is transciency, where the time the experience takes doesnt dictate the significance of the experience, as time is altered or distorted in some way, just as in a dream – the dream may seem really long, whereas in reality its only been a few minutesShow MoreRelatedDiscussion of D.Z . Phillips Conception of Immortality Essay1087 Words   |  5 Pagescommon sense, conceptions of what immortality means. Phillips argues that philosophical analyses centred on the notion of immortality have generally been constructed around certain essential presuppositions: presuppositions that assume some form of continuation of personal identity after death. 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The Railroads Role in the Settling of the West Free Essays

string(59) " of strikes occurred at the end of the nineteenth century\." One of the largest contributing factors in the settling of the American West was the completion of the transcontinental railroad. Development was a slow process in much of the west, due in large part to how long the journey took. The completion of the railroad made it both a faster and much safer way to travel across the country. We will write a custom essay sample on The Railroads Role in the Settling of the West or any similar topic only for you Order Now In 1862, the Pacific Railroad Act was signed. It promised federal support to build the first transcontinental railroad. Two companies were chosen to take on this enormous project, they were awarded generous land grants and were given millions of dollars in government loans so that they could complete the project. The Union Pacific Railroad started laying tracks heading west from Iowa, while the Central Pacific Railroad was laying tracks heading east from California. The two sets of tracks finally merged together in Promontory, Utah on May 10, 1869, creating the first transcontinental railroad. Before the completion of the railroad travel to the west was primarily done by horseback or wagon train. This type of travel took several months to complete and was a very strenuous and dangerous journey, especially when travelling through Indian country. After completion of the railroad the same trip was reduced to a week’s time, while making it a far less dangerous trip especially for the women and children. Passengers were offered free trips, along with long term loans from the railroad companies. This was all done in an effort to attract Americans to the newly developing west. Railroad company executives no longer viewed the Great Plains which covered much of the American West as the inhabitable Great American Desert as it had once been described. The vast native grasslands that are so predominant in Kansas, Colorado, Wyoming, Montana, and the Dakotas that was once thought of as unlivable tracts of land due to the lack of trees to supply lumber that was needed for building homes. There was now an opportunity to ship lumber and building materials into those areas by train, and homes could be built on land that was once considered inhabitable. These native grasslands lands were also considered to be an ideal place for raising cattle. There were already an estimated five million head of longhorn cattle on ranches in Texas. When railroad tracks reached Missouri, these ranchers started organizing long cattle drives. Cowboys would drive the cattle from Texas to Missouri, where it was then loaded into rail cars to be shipped all over the country. As new tracks were being laid, new towns were being built in the areas that the tracks ran through. Within a few years, Abiline, Witchita, and Dodge City all sprang up in Kansas. These towns were all established due to the cattle trade that was created from the railroads, and thrived off of the business provided by the cowboys and the railroad employees. So in conclusion, a few of the railroads contributions to the settlement of the American West. Before the railroad, travel to the west was done on horseback, it took months of traveling over dangerous terrain. After the railroad, travel to the by rail was done in a week’s time on the safety of a train. Lumber and building supplies were now able to be shipped to the Great Plains, a place once thought inhabitable due to the lack of trees that were needed for building homes. Lastly, the railroad allowed the long cattle drives to take place that were responsible for building many towns where the railroad passed thru. There were other contributions that contributed to the settlement of the Great West but I believe these are some of the most significant. Why the AFL Prevailed Over the Knights of Labor One of the main reasons that the American Federation of Labor (AFL) was able to prevail over the Knights of labor was due to the fact that they understood the need for power. This power was achieved by a couple of different ways, they limited their membership to skilled workers, and they did not engage in politics. Their goals were simple, above everything else, the union was there to protect the worker’s rights. The AFL was the national labor union for skilled workers, and they restricted their membership to skilled workers, most of whom were in the craft trade. With all of their members being skilled workers, it gave them solidarity, and meant that all of the members were interested in achieving the same goals. Unlike the Knights of Labor, who would allow membership to all wage earners except lawyers and saloon keepers. This made their membership to widespread, a result of this meant that not all the Knights members were interested in the same objectives. One of the reasons the AFL gained an advantage over the Knights was because of the AFL’s member restrictions. Samuel Gompers was appointed president of the AFL in December of 1886. Gompers realized the importance of keeping things simple. He understood that what was most important to the majority of workers was higher wages and better working conditions. Gompers made sure that the union’s first priority was to protect the rights of the workers. 1 His refusal to let the AFL delve into the political arena allowed them to maintain the support of both the government, and the public. One tactic that was used by unions were boycotts, these were able to take place because of the public’s support for the workers issues. Unions would hold town meetings explaining the workers grievances with their employers, the public would show their support by refusing to buy products that were produced by the company being boycotted. Of course the most popular tactic used by the union was the strike. Employees would refuse to work and form a picket line if the union was unable to reach a collective bargaining agreement with the employer. Thousands of strikes occurred at the end of the nineteenth century. You read "The Railroads Role in the Settling of the West" in category "Papers" The large and growing size of the AFL was used to support these strikes. Unions only won about half of these strikes, but their demands were either partially or fully met in many cases. The AFL was the dominant national labor union in the United States, until the Great Depression. 2 In conclusion, the AFL was able to prevail over the Knights of labor because of the power and solidarity they gained by limiting their membership to skilled workers. By realizing that most workers goals were simple ones that included better pay, and working conditions. Also because of public support that allowed them to conduct boycotts and strikes that would better the lives of the workers that were members. The Significance of technological innovation in Building American Cities American cities were significantly affected by technological advances in the later part of the nineteenth and the beginning of the twentieth century. These advances were major contributors to the development of the modern city that we see in America and throughout the world. They were a crucial part in allowing cities to be able to grow and support the millions of people that reside in them. Generating technology made it possible to use electricity for improvements in the city. In 1878 the electric arc lamp was first used in Wanamaker’s department store in Philadelphia. This form of electricity was then used to power city lights, and later, elevators, trolley cars, and subways. Trolley cars were the first forms public transit used in cities that was powered by electricity. Trolleys ran on steel tracks and were powered by an electrical cable that ran above them. This however was not a viable mode of transportation in some of the larger more populated cities. Railroads had been the principal mode of transportation for the past few decades, but were of little use for transporting people through a crowded city. That is, until 1879, when the creation of the first elevated railroad or â€Å"els† took place in New York. Cities were also constructing rail systems that ran underground. Boston was the first to use this transportation method, but in 1904, New York completed construction of the first subway system that ran under the entire length of Manhattan. Subways used the same electric technology that was used for trolleys, but they turned public, or mass transit into a much more rapid form of transportation. New innovations in the steel and glass industries allowed architects to change their way of thinking in regard to building design. Instead of using just wood or brick for the outside walls that would bear much of the buildings weight, they were now using steel girders. These girders would be used to build a shell that supported the buildings weight, and the rest of the building was built around them with brick and plate glass windows and other building material. This new building design allowed the construction to reach much higher into the sky. The first building using this new design was built in Chicago in 1885, the ten story Home Insurance Building. Later New York, which was heavy in population but low on available real estate built the fifty-five story Woolworth Building that was completed in 1913. 3 In conclusion, technological innovations significantly affected the building of American cities. Generated technology allowed the use electricity to power our lights, elevators, and subways. Creative thinking in the way that we used the railroads spurned the first subway system. While advances in the steel and glass industries gave architects the opportunity to design the skyscrapers that dot the skyline of American cities. Free Silver and the 1896 Election Free silver was a very heated topic during the Presidential election in 1896, due to the economic crisis that the country was in. Because of the governments shrinking gold reserves it was proposed that silver be used at an exchange rate of sixteen ounces of silver, equaling one ounce of gold. Free silver was the term being used for this concept. It was widely thought, especially among Democrats, that this influx of silver would help to propel the country out of the depression and economic despair of the last three years. Farmers were going bankrupt, thousands of Americans were unemployed, and the economy did not appear to be getting better unless changes were made. These are the issues that brought free silver to the forefront of politics. This issue gained much of its support from the wheat and grain farmers in the Midwest and by the cotton farmers from the South. These farmers were being hurt financially due to falling prices for their crops. The economy in the United States was in need of dire repair and many people saw silver as the economic boost that was needed. Free silver had become the most debated topic leading up to the Presidential election. Democrats wanted to go back to a bimetallic policy for the United States Treasury Department. They believed that this was the only solution to end the economic crisis that the country had been in for the last three years. This was not the first time that silver was a heated topic, this had been an area of debate since it was dropped as a medium of exchange at the treasury in 1873. Democrats had become the party of free silver, but the parties were becoming divided based upon whether members were in support of gold or in support of silver. Free silver however was not just getting support from the Democrats, many Republicans were also in support of silver, and both Democrats and Republicans were switching parties over this debate. Populists, who were also in strong support of the silver were essentially turned into Democrats. This had become one of the most heavily debated subjects in the later part of the nineteenth century and it made the election of 1896 one of the most hard fought campaigns in nearly since 1860. 4 In conclusion, free silver had become such a hot topic during the election of 1886 due to the economic crisis the country was in. Many people believed that free silver was the solution that would give the economy the boost that it needed. Lastly, the silver debate was such a hot topic that it caused both Democrats and Republicans to jump parties over the issue. How to cite The Railroads Role in the Settling of the West, Papers

Legal Aspects of International Lagal Trade and Enterprise

Question: Discuss about the Legal Aspects of International Lagal Trade and Enterprise. Answer: Introduction: The legal aspects of International Trade introduce the complex international legal framework that enables the individuals, business organisation and the governments for exchanging the products and the services legally and successfully. According to the opinion of Barker et al. (2009), the international Trades legal aspects assist to offer a managerial perspectives and awareness regarding the legal implications. The specific action often assisted the Australian International Trade measures to increase its accessibility in the internal market segment. The study attempts to identify the legal aspects of international trade for an organisation which has the business operation in Australia. Considering the fact, the research associate has chosen the company, BHP Billiton Ltd., which is a multinational mining, metals and petroleum company. The regulatory framework of Australian government and the trade union has been identified in the current study to scrutinize the operational impact on t he company. Furthermore, identification of the treaties, conventions and the other agreements that have direct impact on the products and services offered by the multinational firm has been analysed in the present research. Body: BHP Billiton is a Melbourne based global mining company. The minerals segment of the company focusing on copper, coal, iron core and nickel in the Australian business that includes operations in Queensland, Westen Australia, South Australia and the New South Wales. In the addition, the operational capability and the technical expertise of BHP Billiton are the petroleum business that includes exploration, production and the development in the USA, Trinidad and Australia. As per the report of the Australian statistics, the number of employees of the firm was 43,238 in 2012, 46,892 in 2013 and 47,044 in 2014 (www.statista.com, 2016). According to the opinion of Cahoy (2008), the firm has a talented, dedicated and skilled workforce to contribute a better-standardised output. It has been speculated that due to some employment issues the company has reduced globally the number of employees, which was 42,829 in 2015 (www.statista.com, 2016). The global headquarters of BHP Billiton is locate d in Melbourne, Australia and London, UK. Fair trading rule both for the business and the customers are maintained by the statutory framework managed by the Australian government. The Australian Competition and Consumer Commission (ACCC) indicate that BHP Billiton has to offer better quality products with affordable price for drawing the attention of the customers (www.bhpbilliton.com, 2016). Considering the words of Castles (2013), the firm could not produce below quality product range with low price for achieving the customers attention. This is also one of the tactics to avoid the overall tax payment. Thus, the government provides some strict rules and legislation for maintaining the product quality of the organisation. It has been identified that the Australian government has faced a budget deficit in the year of 2014 and 2015. The tax payers of Australia took advantage of "pay as you earn" introduced by the Australian Government (Barker, 2009). The business organisation also takes advantage of this particular law and in vests money on different properties. In this scenario, the government has tightened the rules to increase the number of the payers in Australia. Thus, the government of Australia instructs that the business organisations operating in the country have to pay 30% corporate tax depending on the income. Over the last three years, the Australian Parliament has passed a set of rule and legislation to constrict the rules of the income tax transfer pricing. Considering the opinion of Castles (2013), when a transaction occurs it needs to be made arms length price, to avoid any duplicity. This rule has been made by the Australian government. The law states that the pricing needs to be at par with the market rate. If any deviation occurs, the party would be charged. The recent trend shows that MNCs headquartered in Australia is doing this sort of unethical practice to avoid tax burden. To mitigate this discrepancy, the Australian government has imposed the pricing strategy. Hence, the prices charged have a direct impact on the level of the profits of each entity of the multinational organisation. Therefore, Richardson et al. (2015) stated that the BHP Billiton has to pay different amounts of tax in the respective countries. On the other hand, by applying the arms length principle, it is required for BHP Billiton to price the intra-group products and services between the associated business parties for contributing to the Australian economy. Considering the view of Barker et al. (2009), the concept of arms length transaction ensures both the parties who are involved in the deal and controls the parties as a multinational group. It has been observed that Australia has a national privacy legislation, which is supervised by the Office of the Australian Information Commission (OAIC). It regulates the operational activities of the business and store the personal information and communication (www.austrade.gov.au, 2016). BHP Billiton has to maintain the OAIC legislation in the workplace. Adding to this the Environment Protection and Biodiversity Conservation Act 1999 (EPBC Act), it protects and manage the ecological community through offering a legal framework. The BHP Billiton CSG maintains the up-to-date pra ctices to adhere the EPBC Act. As per the opinion of Castles (2013), success in exploration, development and the other production activities is reinforced by the effective maintenance of the environmental rules. The management of BHP Billiton has managed to introduce certain systems that are entirely aligned with the legal treaties. The brand has also imposed effective controlling measures and operations that justify the viability of the implemented systems. Supporting this Richardson et al. (2015) stated that BHP has a sensitive planning and the effective project design to fulfil the requirement of the Australian Government treaties. Before approving the national environmental and cultural concerns, Australian Government Legislation governs the assessment process of the multinational organisation. Furthermore, the Australian Consumer Law (ACL) offers treaties for the imbalanced contract agreements. The consumer right is administered by the Australian Competition and Consumer Commission (ACCC) and the State and Territory consumer protection agencies of Australia (www.austrade.gov.au, 2016). Moreover, BHP Billiton has entered into a contract with Brazils Federal Attorney General, where the ma nagement claims to provide a compensation for the damage caused for the Samarco tragedy. Conclusion: The Australian government has made a sustainable path to balance the budget by incorporating several corporate for the business organisation. The government has introduced several responsible choices to ensure the overall impact of the new business policies. The mining firm, BHP Billiton adhered to all the rules measured by the Australian government to make the business execution easy. Moreover, adherence to Product liability regulation regulates the product safety of the firm, so that BHP can uphold the sustainable position in the Australian marketplace. References: 2016, S. (2016) Number of employees at BHP Billiton from 2012 to 2015, by region*. Available at: https://www.statista.com/statistics/274234/number-of-employees-at-bhp-billiton-by-region/ (Accessed: 24 August 2016). Barker, R.M., Cobb, A.T. and Karcher, J. (2009) The legal implications of electronic document retention: Changing the rules, Business Horizons, 52(2), pp. 177186. Billiton, B. (2016) BHP Billiton results. Available at: https://www.bhpbilliton.com/ (Accessed: 24 August 2016). Cahoy, D.R. (2008) Treating the legal side effects of cipro: are evaluation of compensation rules for government takings of patent rights, American Business Law Journal, 40(1), pp. 125175. Castles, M. (2013) Australia: Client CapacityInadequate rules and unpalatable choices, Legal Ethics, 16(2), pp. 367369. Commission, A.T. (2016) Australian business and environment laws. Available at: https://www.austrade.gov.au/International/Invest/Guide-to-investing/Running-a-business/Understanding-Australian-business-regulation/Australian-business-and-environment-laws (Accessed: 24 August 2016). Richardson, G., Taylor, G. and Lanis, R. (2015) The impact of financial distress on corporate tax avoidance spanning the global financial crisis: Evidence from Australia, Economic Modelling, 44(12), pp. 4453. Taylor, G. and Richardson, G. (2014) Incentives for corporate tax planning and reporting: Empirical evidence from Australia, Journal of Contemporary Accounting Economics, 10(1), pp. 115.