Determining Outliers in Statistics

Outliers are data values that differ greatly from the majority of a set of data. These values fall outside of an overall trend that is present in the data.  A careful examination of a set of data to look for outliers causes some difficulty. Although it is easy to see, possibly by use of a stemplot, that some values differ from the rest of the data, how much different does the value have to be to be considered an outlier?  We will look at a specific measurement that will give us an objective standard of what constitutes an outlier. Interquartile Range The interquartile range is what we can use to determine if an extreme value is indeed an outlier. The interquartile range is based upon part of the five-number summary of a data set, namely the first quartile and the third quartile. The calculation of the interquartile range involves a single arithmetic operation. All that we have to do to find the interquartile range is to subtract the first quartile from the third quartile. The resulting difference tells us how spread out the middle half of our data is. Determining Outliers Multiplying the interquartile range (IQR) by 1.5 will give us a way to determine whether a certain value is an outlier. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers. Similarly, if we add 1.5 x IQR to the third quartile, any data values that are greater than this number are considered outliers. Strong Outliers Some outliers show extreme deviation from the rest of a data set. In these cases we can take the steps from above, changing only the number that we multiply the IQR by, and define a certain type of outlier. If we subtract 3.0 x IQR from the first quartile, any point that is below this number is called a strong outlier. In the same way, the addition of 3.0 x IQR to the third quartile allows us to define strong outliers by looking at points which are greater than this number. Weak Outliers Besides strong outliers, there is another category for outliers. If a data value is an outlier, but not a strong outlier, then we say that the value is a weak outlier. We will look at these concepts by exploring a few examples. Example 1 First, suppose that we have the data set {1, 2, 2, 3, 3, 4, 5, 5, 9}. The number 9 certainly looks like it could be an outlier. It is much greater than any other value from the rest of the set. To objectively determine if 9 is an outlier, we use the above methods. The first quartile is 2 and the third quartile is 5, which means that the interquartile range is 3. We multiply the interquartile range by 1.5, obtaining 4.5, and then add this number to the third quartile. The result, 9.5, is greater than any of our data values. Therefore there are no outliers. Example 2 Now we look at the same data set as before, with the exception that the largest value is 10 rather than 9: {1, 2, 2, 3, 3, 4, 5, 5, 10}. The first quartile, third quartile, and interquartile range are identical to example 1. When we add 1.5 x IQR 4.5 to the third quartile, the sum is 9.5. Since 10 is greater than 9.5 it is considered an outlier. Is 10 a strong or weak outlier? For this, we need to look at 3 x IQR 9. When we add 9 to the third quartile, we end up with a sum of 14. Since 10 is not greater than 14, it is not a strong outlier. Thus we conclude that 10 is a weak outlier. Reasons for Identifying Outliers We always need to be on the lookout for outliers. Sometimes they are caused by an error. Other times outliers indicate the presence of a previously unknown phenomenon. Another reason that we need to be diligent about checking for outliers is because of all the descriptive statistics that are sensitive to outliers. The mean, standard deviation and correlation coefficient for paired data are just a few of these types of statistics.

Math Worksheets Multiplication Magic Squares

Effects Of Alcohol Abuse And Alcoholism - 1446 Words

When entering the field of social work, a person should understand the effects of alcohol, not only on an individual, but also the effects on the families. Alcohol is one of the many substances that people use and abuse. Since alcohol is legal for any one over the age of twenty-one, many people begin drinking and then develop an addiction to the substance (Goldberg, 2016). Alcoholism effects people of all ages, background, social status, or ethnic group (National Institute on Drug Abuse, 2016). A social worker should understand how to assess and intervene families who are struggling with alcohol addiction in a way that is both ethical and culturally competent (National Institute on Alcohol Abuse and Alcoholism, 2005). The main goal for a social worker is to promote well-being and help provide the basic needs of all people (National Association of Social Workers, 2008). To begin, a social worker must first assess the situation that is before them and collect as much information as pos sible. Several questions need to be asked to either the family or the person who has alcoholism. For example, on average, how many days a week does the person consume alcohol? On those days, how many alcoholic beverages are consumed? In the last thirty days how many times have you had more than four alcoholic beverages? These questions need to be asked first because a social worker needs to know how severe the problem is (National Institute on Alcohol Abuse and Alcoholism, 2005). In some casesShow MoreRelatedAlcoholism : A Growing Problem1468 Words   |  6 PagesAlcoholism Alcoholism is a growing problem in today s society. What is alcoholism? Is it a disease? What are the causes of it? What toll does alcohol abuse have on individuals? American society? American economy? What kind of treatments are available to reduce/cure alcoholism? What is alcoholism? 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Global Business Maintaining Sustainability

Question: Discuss about theGlobal Business for Maintaining Sustainability. Answer: Introduction: Globalization is a trend that is adopted by domestic companies for maintaining sustainability and expansion of business operations in foreign markets. The essay focuses on various drivers of globalization that will encourage local businesses of different countries to spread their reach in the global market. However, the adaptation of globalization is a challenging task for small, medium enterprises. Decisions regarding expansion are to be taken after conducting an extensive market research on different aspects of the target foreign market. Apart from that, two economic theories of absolute advantage and comparative advantage are explained in the perspective of companies expansion in international markets. The thesis statement of the essay is to describe globalization as a growth factor for domestic businesses in the light of comparative and absolute advantage theories. Both the topics of globalization and the economic theories are related with one another in the sphere of business ex pansion of domestic companies. With the increase of competition in the market, the economic outlook of different countries is blurring. It leads to a looming squeeze in the prospect of business in various sectors. Markets are becoming competitive with slowing growth, shortages of right talents and complexity in operational activities. Domestic companies of different countries are facing many challenges for sustaining in the competitive market. Globalization is the process where companies start operating their business operations on a global scale (Liang, Ren and Sun, 2015). There are different types of globalization such as economic, cultural, political, and environmental globalization. However, domestic companies operate in economic globalization usually to enter into a new market. The increase of competition in the market pushes companies for becoming global. Economic globalization trends are accounted in developed economies with the integration of lower developed economies (Vahlne and Ivarsson, 2014). It happen s to foreign direct investment and reduction in economic reforms, trade barriers, and immigration. The government of many countries provides scope to many companies for doing business in their countries. Glocalization is another concept related to globalization. Glocalization means adopting local flavors in the target market. Domestic companies conduct their business on the considerations of both local and global level. However, the adaptation of these two concepts will help national companies for achieving maximum profit and brand awareness in the market. For instance, McDonalds is an American fast food retail chain that operates in almost 119 countries around the world. The first store of the company was opened in the United States of America. Slowly, adopting various strategies of glocalization in international businesses, McDonalds has started operating on a global scale. In the first phase of its expansion, the company chooses globalization policies. However, soft drinks, fast food restaurants have permissions in operating their business in almost all countries (Zaman, Selim and Joarder, 2013). There are many organizations such as aircraft manufacturing companies do not have permissions to spread their business in particular countries. Alphapharm is an Australian based pharmaceutical company. The enterprise has its dominance in many parts of Australia. However, it is operating over 50 countries across the world. This company also adopted globalization for earning more revenue. A domestic company steps into international markets due to many reasons such as saturation of the national market, expansion of business, increase of brand awareness, etc. Alphapharm caters medicines to many countries based on the customer needs (Moir, 2015). Variations of marketing strategies are required to mitigate the needs of the clients in the target market. In economics, absolute advantage and comparative advantage are the theories that firms apply during the time of internalization. The two ideas are related to the concept of globalization. Adam Smith proposes absolute advantage theory in the perspective of international trade. The theory of absolute advantage suggests the capacity of a country or a firm to produce the maximum amount of product or service using the same amount of raw materials and resources (Levchenko and Zhang, 2016). The model considers labor as an input. Labour productiveness is determined by using simple comparisons in the theory of absolute advantage. Since the theory only considers labor productivity; a country can achieve zero absolute advantage while operating in a foreign market. According to Adam Smith, the wealth of a country depends on the amount of resources available in the country including the gold reserves of a country (McGrath, 2013). If a company is enjoying absolute advantage, then it will run in pr ofit in its international operations. On the other hand, if a company has zero absolute advantage, then the company is not able to make any trade with another party in the new target market. For instance, a company operating in England requires 50 hours of labor work to produce a single unit of cloth. However, in Portugal, another company requires 80 hours of work to manufacture the same amount of material. Then it can be said that the enterprise of England has a greater competitive advantage than the enterprise of Portugal. The comparative advantage of economics is a theory that refers to the productivity of a firm at a lower opportunity cost and lower marginal costs. Many factors influence comparative advantage of companies or countries such as technological aspect, political conditions, etc. David Ricardo proposes the theory of comparative advantage. According to David, comparative advantage is more helpful regarding international trade when compared to absolute advantage. Input cost is a vital aspect in manufacturing goods in the global market (Irwin, 2015). If the cost of production rises, then the company will not be able to generate a substantial amount of profit in the market. Companies must not compare the costs of resources and commercial production costs. Instead of it, businesses can compare opportunity costs among different countries. The concept of free trade is related to the theory of comparative advantage (Paliwoda and Thomas, 2013). Under the free trade, the company having a greater com petitive advantage can produce more amounts of products along with consuming lesser amount of products. The two theories of an economy are related to each other but have many differences. Comparative advantage Absolute Advantage Comparative advantage means a varied level of opportunity costs. Absolute advantage means differences in the level of productivity of firms or nations. Comparative advantage includes opportunity costs. Absolute advantage considers labor as an input. A company having greater absolute advantage may not have a greater comparative advantage (Buera and Kaboski, 2012). Firms or countries having more significant comparative advantage have the possibility of having the greater absolute advantage also. Comparative advantage is followed by most of the companies in the world while less number of businesses follows absolute advantage theory. In absolute advantage theory, mutual beneficial of trade is not a possibility whereas trade is mutually benefitted in the theory of comparative advantage (Huxham and Vangen, 2013). Comparative advantage consists of the production output of the same category of products between two countries. On the contrary, absolute advantage refers to more amount of goods using the same amount of resources and materials in an efficient way. Comparative advantages related with the overall techniques of manufacturing goods within a stipulated period (Cuat and Melitz, 2012). Absolute advantage is concerned with the production of multiple products or services. Opportunity cost is involved in the theory of comparative advantage. Labor cost intervenes in absolute advantage. Apart from having advantages, there are some limitations of these theories. Both the approaches are feasible for two countries, firms, and goods. The two theories are not possible for a large number of products and countries. When the economies of two countries are at same level, only when these principles can be implemented. The employment structure of a country may have a direct impact on determining absolute advantage of a state that is a restraint factor. In the sphere of comparative advantage, the opportunity cost is a common factor that varied at a different level (Kapoor and Adner, 2012). The cost of transport is the reason of outweighing any types of comparative advantage. Restrictions of government and regulations can restrict businesses and trade in an international scale. It can hinder the implementation of economic theories by firms or countries. Diseconomies of scale are the cause of increased specialization of products by countries or enterprises. Another limitation of comparative advantage is it does not measure dynamic advantage i.e. future scope of the country. It only measures static advantage of the firm. The essay describes various concepts of globalization and different economic theories of international trade. It also fosters the thesis statement that is mentioned above. Along with globalization, the idea of glocalization is also described. Specific examples are provided in the study that illustrates the domestic companies' reason for adoption of international strategies. Apart from that, advantages and disadvantages of both comparative and absolute advantage in the practical field are demonstrated by providing proper examples. Local companies on internalization choose different types of globalization approaches. Among the various methods, economic approach is the most suitable approach that considers many factors of globalization. Relation of the two theories of economics along with the limitations is explained in a detailed manner in the essay. National companies following the above three concepts of international trade certainly earn huge revenue in its business operations in th e target market. References Buera, F.J. and Kaboski, J., 2012. The rise of the service economy.The American Economic Review,102(6), pp.2540-2569. Cuat, A. and Melitz, M.J., 2012. Volatility, labor market flexibility, and the pattern of comparative advantage.Journal of the European Economic Association,10(2), pp.225-254. Huxham, C. and Vangen, S., 2013.Managing to collaborate: The theory and practice of collaborative advantage. Routledge. Irwin, D.A., 2015.Free trade under fire. Princeton University Press. Kapoor, R. and Adner, R., 2012. What firms make vs. what they know: how firms' production and knowledge boundaries affect competitive advantage in the face of technological change.Organization Science,23(5), pp.1227-1248. Levchenko, A.A. and Zhang, J., 2016. The evolution of comparative advantage: Measurement and welfare implications.Journal of Monetary Economics,78, pp.96-111. Liang, H., Ren, B. and Sun, S.L., 2015. An anatomy of state control in the globalization of state-owned enterprises.Journal of International Business Studies,46(2), pp.223-240. McGrath, R.G., 2013.The end of competitive advantage: How to keep your strategy moving as fast as your business. Harvard Business Review Press. Moir, H.V., 2015. The patent price of market access in the AUSFTA.Australian Journal of International Affairs,69(5), pp.559-576. Paliwoda, S. and Thomas, M., 2013.International marketing. Routledge. Vahlne, J.E. and Ivarsson, I., 2014. The globalization of Swedish MNEs: Empirical evidence and theoretical explanations.Journal of International Business Studies,45(3), pp.227-247. Zaman, S., Selim, N. and Joarder, T., 2013. McDonaldization without a McDonald's: Globalization and Food Culture As Social Determinants of Health in Urban Bangladesh.Food, Culture Society,16(4), pp.551-568.