What Is Kurtosis in Statistics

Distributions of data and probability distributions are not all the same shape. Some are asymmetric and skewed to the left or to the right. Other distributions are bimodal and have two peaks. Another feature to consider when talking about a distribution is the shape of the tails of the distribution on the far left and the far right. Kurtosis is the measure of the thickness or heaviness of the tails of a distribution. The kurtosis of a distribution is in one of three categories of classification: MesokurticLeptokurticPlatykurtic We will consider each of these classifications in turn. Our examination of these categories will not be as precise as we could be if we used the technical mathematical definition of kurtosis. Mesokurtic Kurtosis is typically measured with respect to the normal distribution. A distribution that has tails shaped in roughly the same way as any normal distribution, not just the standard normal distribution, is said to be mesokurtic. The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. Besides normal distributions, binomial distributions for which p is close to 1/2 are considered to be mesokurtic. Leptokurtic A leptokurtic distribution is one that has kurtosis greater than a mesokurtic distribution. Leptokurtic distributions are sometimes identified by peaks that are thin and tall. The tails of these distributions, to both the right and the left, are thick and heavy. Leptokurtic distributions are named by the prefix lepto meaning skinny. There are many examples of leptokurtic distributions. One of the most well known leptokurtic distributions is Students t distribution. Platykurtic The third classification for kurtosis is platykurtic. Platykurtic distributions are those that have slender tails. Many times they possess a peak lower than a mesokurtic distribution. The name of these types of distributions come from the meaning of the prefix platy meaning broad. All uniform distributions are platykurtic. In addition to this, the discrete probability distribution from a single flip of a coin is platykurtic. Calculation of Kurtosis These classifications of kurtosis are still somewhat subjective and qualitative. While we might be able to see that a distribution has thicker tails than a normal distribution, what if we don’t have the graph of a normal distribution to compare with? What if we want to say that one distribution is more leptokurtic than another? To answer these kinds of questions we need not just a qualitative description of kurtosis, but a quantitative measure. The formula used is ÃŽ ¼4/ÏÆ'4 where ÃŽ ¼4 is Pearson’s fourth moment about the mean and sigma is the standard deviation. Excess Kurtosis Now that we have a way to calculate kurtosis, we can compare the values obtained rather than shapes. The normal distribution is found to have a kurtosis of three. This now becomes our basis for mesokurtic distributions. A distribution with kurtosis greater than three is leptokurtic and a distribution with kurtosis less than three is platykurtic. Since we treat a mesokurtic distribution as a baseline for our other distributions, we can subtract three from our standard calculation for kurtosis. The formula ÃŽ ¼4/ÏÆ'4 - 3 is the formula for excess kurtosis. We could then classify a distribution from its excess kurtosis: Mesokurtic distributions have excess kurtosis of zero.Platykurtic distributions have negative excess kurtosis.Leptokurtic distributions have positive excess kurtosis. A Note on the Name The word kurtosis seems odd on the first or second reading. It actually makes sense, but we need to know Greek to recognize this. Kurtosis is derived from a transliteration of the Greek word kurtos. This Greek word has the meaning arched or bulging, making it an apt description of the concept known as kurtosis.

A Critical Analysis regarding the Innovation Management Practices Adopted by Apple Inc. and Haier Group Free Essay Example, 3500 words

The company has shown a constant openness to new ideas, as they believe that new ideas are not only limited to new product development but are equally significant for the improvement of business processes. The firm believes in this principle has produced highly satisfactory results for the company and by the end of the year 2010. The number of patents and innovation are highest for this company among the Chinese manufacturers (Yuanyuan 2011). A series of initiatives have been taken by the company to promote innovation and creativity at the workplace. All these initiatives of the company revolve around quality and customer satisfaction. An example shows how the company has emphasized upon providing high quality to consumers when it decided to set a quality benchmark even above the Japanese Industrial Standard (JIS). As per the guidelines of JIS, the return-repair ratio for refrigerator should be less than 0.6%, as against this stringent benchmark of JIS, the company decided to set th e same ratio at the level of 0.4%. As a result of this decision the company in the year 1988, Haier was awarded China s National Quality Gold Medal. We will write a custom essay sample on A Critical Analysis regarding the Innovation Management Practices Adopted by Apple Inc. and Haier Group or any topic specifically for you Only $17.96 $11.86/page The management philosophy of OEC was introduced in the year 1986 and became famous with the name of All around Optimized Management Approach (TU and YUAN 2010). The OEC plan was driven by the purpose of effective management of everyday business processes and enabled Haier in evaluating the appropriateness of the plan in terms of produced outcomes.

The Advocacy For Lgbt Community - 1380 Words

Description of the importance of the topic The topic on the advocacy for LGBT community in schools among the student community is very important. In most cases the advocates of LGBTs have tried to persuade schools to improve their environment. Usually the school environment significantly determines whether the climate in the school is healthy and appropriate for LGBT students to learn in (Goldberg and Allen, 2013). Advocating for this community therefore means that school administrators are likely to adopt ignored programs that may concern the issues of sexual orientation and gender identity. Such initiatives improve the schooling environment for the diverse population of all the students regardless of their sexual orientation. Advocating for the LGBT students helps in fighting discrimination, in regard to the legal requirements many schools fail to recognize the sexual minority students hence failing to address issues that affect the safety as well as the education of the LGBT stude nts. Advocacy on legal requirement for the schools is for instance based on the 14th Amendment of the US constitution (Jacob, et al. 2011). It states that all the students are entitled to equal protection under the federal law without any discrimination. This helps the students attain the education they deserve with no restrictions. The training of the staff members helps in understanding the sexual minority students and the use of effective interventions. 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Financial problem among student free essay sample

Students In Financial Crisis: How Academic Advisers Can Help Reed T. Curtis. university of South Carolina Editors note: This Is the eighth In a series of articles written by students enrolled In Jennifer Blooms graduate seminar on academic advising at the university of South Carolina for the 2007 fall semester. As part of her course syllabus, Dr. Bloom required each student in her class to submit an article to The Mentor or other publications for consideration. Introduction Given that tuition and fees at colleges and universities are rising at a pace hgher han the cost of living, students face an Increasingly difficult burden of funding their educational pursuits. Since the 1980s, the cost of higher education has skyrocketed; college tuition and fees have risen by 375 percent, while the average household income rose only 127 percent (Hunt et al. , 2006, p. 19). According to a 2006 united States Department of Education report, Our higher education financing system Is increasingly dysfunctional [as] state subsidies are declining, tuition is rising, and cost per student is increasing faster than inflation or family income (p. 0). This report also found that state funding of education hit a new low in 2005. All of these factors have led to unprecedented levels of debt for college graduates. King and Bannon (2002) reported that 64 percent of college students graduate with debt; 39 percent of them have debt that is deemed unmanageable. King and Bannon define unmanageable student-loan debt as a debt load that exceeds 8 percent of a graduates pre-tax yearly income. Minorities are more likely to have an unmanageable student-loan debt. Fifty-five percent of African American and 58 ercent of Hispanic graduates compared to only 37 percent of Caucasians graduated with unmanageable debt (King Bannon, 2002). Another Indicator of the extent of this problem is that 60 percent of college students move back in with their parents after graduation, helping to define a growing trend coined as the boomerang generation (Experience Inc. 2006). Graduates reasons for moving home after graduation vary, but 48 percent of boomerangers move home because of financial problems (Experience Inc. , 2006). As The Project on Student Debt (2007) explains, the prospect of student debt can prompt students to compromise on ollege choice, drop out, or forego higher education altogether (p. 13). In fact, students who lack financial security are more l ikely to do worse In college, drop out, or even commit suicide Oohnson, 2005). The purpose of this article is to stress that strengthening financial literacy among academic advisers Is now a critical aspect of working with and empowering todays college students. IOF6 lypes 0T student De It is also important to understand that student debt is diversified and is not simply linked to student loans alone. Students are now increasingly using credit cards to over additional college and life expenses Oohnson, 2005). In 2004, 66 percent of all first-year students already had at least one credit card before stepping foot into their first college classroom (Nellie Mae, 2005). Even more alarming is the fact that the number of credit cards students possess increases each year throughout college, with 56 percent of seniors carrying four or more cards compared to 15 percent of first-year students with four or more (Nellie Mae, 2005). Reasons for this increased student dependence on credit cards include heavy credit-card solicitation, easy ccess to credit cards, increased living and school expenses, and lack of financial literacy Oohnson, 2005). Credit card companies are tireless solicitors of college students despite campus regulations and other measures of prevention Oohnson, 2005). Here are Just some of the issues that relate to credit card use and abuse on college campuses: The Collection: Credit card companies participate in aggressive and emotionally abusive efforts to collect payments. This becomes a huge distraction for students who may already be struggling in school. In the face of these mounting inancial pressures, some students may get additional student loans to pay their credit card bills, some take on additional Jobs that reduce time for academic studies and extracurricular opportunities, some students drop out of school to earn more money, some become depressed and some of those even attempt to or do commit suicide Oohnson, 2005), and others are forced to declare bankruptcy. Bankruptcy rates tripled between 1995 to 2000 among people younger than 26 years old Oohnson, 2005). Stigmatization: Students feel alone in their financial crises and sometimes are too embarrassed to seek advice from others. Many do not feel comfortable telling people about their situation, because they feel that others will see them as stupid or completely irresponsible. Going to their parents may seem to be a plausible option, but many students fear their parents anticipated disappointment and anger, and thus feel completely alone when faced with mounting bills, classroom assignments, living expenses, and expectations Oohnson, 2005). The Burden: In most cases, there are no easy solutions to student debt loads. Students begin to recognize the lifelong implications of their previous financial decisions. The financial situation becomes constant and requires lifestyle changes, some of which limit students ability to academically succeed Oohnson, 2005). The burden of credit card debt haunts many students and can lead to a multitude of problems. A student stressed over credit card debt may suffer additional financial, psychological, and physical problems Oohnson, 2005, p. 209). Because students financial instability during college can lead to depression and suicide Oohnson, 2005), advisers should be on the lookout for warning signs and know how to effectively refer students to mental health services. Academic advisers should also be aware of the increased risks of financial instability among minorities and establish communication wltn tne multlcultural servlces avallaDle on campus. As advisers, it is extremely important to have a basic understanding of the higher- education financial climate and the ways that students can obtain aid (Sutton, 2002; Moran, 2002). With the help of academic advisers, college students may be able to avoid financial disasters. Education Advisers should work Just as hard to encourage and instill financial literacy in advisees as they impart tips for academic success.