How dependent are Americans on foreign oil Essay Example for Free

How dependent are Americans on foreign oil Essay 1.0 Introduction â€Å"We have a serious problem. America is addicted to oil.† George Bush made this assertion in his 2006 State of the Union address. By 2025 the United States will increase its daily consumption of oil to 28.3 million barrels per day. These estimates by the Energy Information Administration (EIA) show that by then, the US will depend on foreign countries for 70% of its oil needs. The United States of America (USA) depends on foreign nations for 66% of the oil it consumes. According to the EIA, currently the US consumes almost 21 million barrels of oil a day. Unfortunately, this amount of oil is not produced locally so the US has to depend on foreign nations for its consumption of oil. The dependence on oil by the US has a number of effects which include: impact on the nation’s economy; determines US foreign policy; shapes national security; and influences the relationship between the US and other nations (Ebe 2). The aforementioned effect which dependence on foreign oil has caused creates problems for the US. One of the major problems is the fact that the US is dependent on other nations for its energy supplies. Since the US is dependent on these nations for oil, the events in these oil producing nations determine to a large extent, what happens in the US. There is need for the US to resolve this energy situation, because dependence on other nations for oil rids the US of its sovereignty as an independent nation. 1.1 Statement of problem Oil is a very useful resource as it used by many industries. Many industrialized nations of the world, like the US, need large amounts of oil to keep their economies going. Over time, the US has become dependent on foreign nations for its oil needs- while local oil production has plummeted, demand is on the rise. Since the US is so dependent on foreign oil, what are the implications of this dependence? 1.2 Dependence on foreign oil: an effects analysis The dependence on foreign oil by the US has a lot of implications. The effect of this situation makes an impact on the economy, foreign policy, national security and international relations. These four perspectives are explored in further detail below. Effects on the US economy. Dependence on foreign oil supplies has had a profound effect on the US economy. One major evidence of this fact is the constant fluctuation of prices of gas due to changes in prices of oil. In other words, once the price of oil changes, then the price of gas in the US shifts accordingly. This has a profound effect on companies and other businesses that use gas. In the past year, oil prices have soared due to a number of factors in the world. Once these prices climb, it means that the consumer in the US has to pay more for goods and services that are related in one way or other to oil. Changes in the prices of oil in the world create shocks which are felt when prices of goods and services increase. However, the US economy would not have had to deal with these shocks if there wasn’t a high dependence on foreign oil. Furthermore, the constant increase in the price of crude oil in global markets leads to the transfer of huge amounts of money to other cou ntries in foreign trade. US foreign policy. Concerns about US dependence on oil have had an influence on its foreign policy. Various governments are aware of US dependence on foreign oil and have taken moves to protect the integrity of the US. Most people around the world believe that the US meddles in the affairs of other countries especially those in the Middle East because of the oil reserves in these places. If there is instability in the Middle East, it will drastically affect the supply of oil to the US. Thus, in order to protect it’s and ensure the constant flow of foreign oil (upon which the US is dependent), the US government takes measures to ensure peace and rule of law in these places. Haley (9-10) echoes the voice of critics who contend that the U is keen on maintaining stability in the Middle East because of the implication which crisis will cause the US since it relies so heavily on foreign oil. This is evident in the Gulf war and the recent invasion of Iraq. These actions by the US hav e created hatred in the hearts of people in the Middle East towards the US. Impact on national security. The dependence on foreign oil by the US has an impact on its national security as well. It can be argued that the dependence on foreign oil by the US has led it get involved in the affairs of other nations of the world. For example, the Middle East is a region which the US does not ignore and it is in this region that the largest reserves of crude oil abound. The US cannot afford to ignore this region because it needs the oil that is produced from these areas. Sadly, many of these countries are places where there is a lot of unrest and oppressive governments and the US gets a share of violent attacks because it relates with these nations. This situation has brewed hatred in the hearts of many and motivated attacks against the US both home and abroad. With the terror attacks on September 11 2001, the US is aware of the threat to national security and the lives of its citizens at home and abroad. Terrorist groups are aware that oil is the centre of the US e conomy and when they target this sector, they will inadvertently cripple the US economy and bring it to her knees. Relations with other nations. The relationship between the US and other nations is also affected to some extent by the dependence on foreign oil by the US. Apart from the US, other countries in the world have vested interests in oil because they too depend to a large extent on oil. With the collapse of the Soviet Union and other â€Å"iron curtain† countries, China has risen as an industrial giant. These industries are largely fuelled by oil and in order to achieve its aim and remain in the lead, China has improved relations with many oil producing countries and opposes restrictions imposed on these places by the US at the United Nations general assembly. These relationships between the US and other nations are founded upon dependence on oil. The dependence on foreign oil by the US has led to complex relationships between the US and other nations. At close observation, the root cause of these relationships is often not noticeable, but exploring deeper brings out the dependence on oil by the US. On the other hand it is important to look at this issue in another perspective. Most of the countries which produce oil are undemocratic. Infact, some of them have oppressive rulers and since the US depends on foreign oil, these governments become prominent. The fact that they are producers of oil propels them to lime light because the US needs this foreign oil so badly. 1.3 Relevant statistics Certain statistics are important in order to understand the dependence on foreign oil by the US. There was a time in the past when the US was the world’s largest producer of crude oil. But all that has changed now. According to the EIA, Saudi Arabia is the world’s largest exporter of crude oil and will remain so for a while because it holds 24% of the worlds oil reserves. Conversely, the Middle East holds 66% of the world’s oil reserve and supplies 30% of oil in the world. The dependence on foreign oil by the US has been worrisome to past administrations. According to Randall, President Richard Nixon established â€Å"Project Independence† to stop America’s dependence on foreign nations for oil. Furthermore, President Gerald Ford approved the regulation of petroleum prices, established the Strategic Petroleum Reserve and signed the Energy Policy and Conservation Act. On his part, President Jimmy Carter signed the national Energy Act to encourage the development of local sources of energy. 1.4 Probable solutions There is growing need to decrease America’s dependence on foreign oil due to the many problems which the phenomenon poses. It is imperative to develop alternate sources of energy in the US so that dependence on oil can gradually be lifted. Dependence on foreign oil may not be lifted totally but a gradual lifting of this dependence is important. Apart from oil, there are alternate sources of energy which should be explored in the US with the backing of the government and private sector so that these initiatives can be widely adopted. In the first place transportation is a major consumer of gasoline, so cars should be made to run on other sources of power such as electricity which is cleaner and will lower carbon emissions in to the atmosphere. Apart from electricity, wind energy too can be harnessed to power industries. Furthermore, dams built on rivers can generate vast amounts of electricity. Biological fuels too are important and these too need to be developed and used to lessen America’s dependence on oil. The current economic crisis in the world is an indicator to many people to cut costs. However, with the rising cost of crude oil, cost cutting will mean learning to do without crude oil and using other alternate sources of energy. Most of the alternate source of energy mentioned here are not harmful to the environment and the other benefit about them is that they are renewable as well. It does not matter how vast a country’s oil reserves are. There will come a time when these reserves will deplete. If the US continues to depend on foreign oil, what will be done when these countries no longer have oil to sell? The situation is best imagined. 1.5 Conclusion Obviously, the US needs to look else where to satisfy her energy needs. The switch from oil to alternative sources of energy may take a while but the journey of a thousand miles begins with a step. This switch has become all the more important considering the amount of hatred which is shown to everything American, especially by terrorists from the Middle East. Much of the world knows that the US economy is affected by oil supplies- cripple this and you bring the world greatest nation to its knees.

Tuberculosis: Prevalent and Deadly Essay -- Diseases/Disorders

Tuberculosis (TB) is a very prevalent, very contagious, and very deadly disease worldwide. According to the Centers for Disease Control, one third of the population is infected with TB. (Centers for Disease Control Data and statistics) While less common than it has ever been, tuberculosis has seen an upsurge in the last three decades directly related to the AIDS epidemic, but also as a result of the development of many multi-drug-resistant strains. This is of particular concern in developing nations hit hard by AIDS infections, but it is also evidenced in an upswing in the United States. (Nester, Anderson and Roberts) Because of the increase of cases both here and worldwide there has been a concerted effort to limit the number of new infections and to control the spread of it by managing the most at risk populations. Nationally this would include prison populations, people with AIDS, and immigrants from countries where there is a high prevalence of TB. Other risk factors include other immunocompromised groups, including those in hospitals, and poverty. The efforts to combat this disease, via education, vaccine administration, and proper sanitation controls have decreased the spread dramatically. Nationally the decrease began in 1993 (Nester, Anderson and Roberts) and internationally the decrease began in 2010. (United Nations ). Mycobacterium tuberculosis is the bacterium responsible for tuberculosis. The bacterium spreads in the air when a person with the infection coughs or sneezes. There are many cases of people with latent TB infection but who may eventually develop the disease and therefore become vectors for contagion. Weakened immune systems greatly increase the chances for developing the disease, which explains why ... ... even the latent infection with medication, and isolating those who are contagious have done more to control the spread of this oft fatal disease than have one particular vaccination. Works Cited Centers for Disease Control. Tuberculosis. March 2012. 11 March 2012 . National Network for Immunization Information. Tuberculosis. March 2005. March 2012 . Nester, Eugene, et al. Microbiology: A Human Perspective. 7th Edition. New York: McGraw-Hill, 2012. "Tuberculosis." Human Diseases and Conditions. 1 March 2012 . United Nations . "United Nations News Service." 11 October 2011. United Nations News Centre. 12 March 2012 .

A Comparative Essay Between 1984 and Brave New World Essay

It is interesting to note, before anything, the similarities between Brave New World and 1984. Firstly and rather obviously, they are both prophetic novels, they were both written in turbulent times, both suffering changes that could revert the future of the world. When 1984 was written, the world had just gotten out of a second war and the surprising rise of communism and their totalitarian government was frightening most of the western world. In George Orwell’s novel, the main concern seems to be the overtaking of a supreme, socialist totalitarian government/dictatorship. On the other hand, when Brave New World was written, the world had just been swept by a wave of mass production and consumerism, and that too is reflected in Aldous Huxley’s ultra-modern, test-tube baby, sleep-taught society. That is exactly what makes the two novels so alike and so different at the same time. To begin with both authors forecast a society of obedience and compliance, but on one hand, the Brave New World is also driven by consumerism and high advanced technology and drug abuse (soma, to ensure the happiness of the masses), † ‘Now- such is progress- the old men work, the old men copulate, the old men have no time, no leisure from pleasure, not a moment to sit down and think- or even by some unlucky chance such a crevice of time should yawn in the solid substance of their distractions, there is always some, delicious soma half a gramme for half a holiday [†¦] returning when they find themselves on the other side of the crevice, safe on the solid ground of daily labour and distraction†¦'†. Whilst 1984 is a bare, war stricken place with food rations and the like, â€Å"Outside, even through the shut window-pane, the world looked cold. Down the street little eddies of wind were whirling dust and torn papers into spirals, and though the sun was shinning and the sky was blue, there seemed to be no colour in anything, except in the posters that were plastered everywhere.† Both novels also similar in the aspect that most inhabitants do not seem to see a problem with the world they live in, most comply and obey, in Brave New World, most consume, but in both novels, there are the odd sheep. In Brave New World Bernard Marx, † ‘But he’s so ugly!’ [†¦] ‘And then so  small.’ Fanny rebels because he does not fit in made a grimace; smallness was so horribly and typically low-caste.† In 1984, Winston Smith rebels because he does not accept, â€Å"to the future or the past, to a time when thought is free, when men are different from one another and do not live alone- to a time when truth exists and what is done cannot be undone. From the age of uniformity, from the age of solitude, form the age of Big Brother, from the age of doublethink-â€Å". says Winston. Both novel seem to portray societies divided into castes, in 1984 there are three of them the ‘proles’, the ‘outer Party’ and the ‘inner Party’, the ‘proles’ are the uneducated masses, the ‘outer party’ are the medium working class, and the ‘inner party’ are the controllers. In Brave New World, the castes are a bit more literal, four in total, Alphas, intelligent and beautiful, have the high positions, Betas, not quite as ‘perfect’ as the Alphas, Gammas, part of the uneducated masses and finally Epsilons, similar in IQ to oysters, the workers and cleaners. Both novels can be regarded as ‘novels that changed history’, that is, when they were written it seemed that things were headed in the direction that both novels pointed out, and some people considered that it was the novels that ‘opened people’s eyes’ and showed them the way. However, many other people seemed to think that both were equally extreme to have actually concretized themselves.

Measures of dispersion - Free Essay Example

Sample details Pages: 16 Words: 4852 Downloads: 9 Date added: 2017/06/26 Category Statistics Essay Did you like this example? Summery The measure of central tendency, as discussed in the previous chapter tells us only about the characteristics of a particular series. They do not describe any thing on the observations or data entirely. In other wards, measures of central tendency do not tell any thing about the variations that exist in the data of a particular series. Don’t waste time! Our writers will create an original "Measures of dispersion" essay for you Create order To make the concept, let discuss an example. It was found by using formula of mean that the average depth of a river is 6 feet. One cannot confidently enter into the river because in some places the depth may be 12 feet or it may have 3 feet. Thus this type of interpretation by using the measures of central tendency some times proves to be useless. Hence the measure of central tendency alone to measure the characteristics of a series of observations is not sufficient to draw a valid conclusion. With the central value one must know as to how the data is distributed. Different sets of data may have the same measures of central tendency but differ greatly in terms of variation. For this knowledge of central value is not enough to appreciate the nature of distribution of values. Thus there is the requirement of some additional measures along with the measures of central tendency which will describe the spread of the entire set of values along with the central value. One such measure is p opularly called as dispersion or variation. The study of dispersion will enables us to know whether a series is homogeneous (where all the observations remains around the central value) or the observations is heterogeneous (there will be variations in the observations around the central value like 1, 50, 20, 28 etc., where the central value is 33). Hence it can be said that a measure of dispersion describes the spread or scattering of the individual values of a series around its central value. Experts opine different opinion on why the variations in a distribution are so important to consider? Following are some views on validity of the measure of dispersion: Measures of variation provide the researchers some additional information about the behaviour of the series along with the measures of central tendency. With this information one can judge the reliability of the value that is derived by using the measure of central tendency. If the data of the series are widely dispersed, the central location is less representatives of the data as a whole. On the other hand, when the data of a series is less dispersed, the central location is more representative to the entire series. In other wards, a high degree of variation would mean little uniformity whereas a low degree of variation would mean greater uniformity. When the data of a series are widely dispersed, it creates practical problems in executing data. Measure of dispersion helps in understanding and tackling the widely dispersed data. It facilitates to determine the nature and cause of variation in order to control the variation itself. Measures of variation enable comparison to be made of two or more series with regard to their variability. DEFINATION: Following are some definitions defined by different experts on measures of dispersion. L.R. Connor defines measures of dispersion as à ¢Ã¢â€š ¬Ã‹Å"dispersion is the measure extended to which individual items vary. Similarly, Brookes and Dick opines it as à ¢Ã¢â€š ¬Ã‹Å"dispersion or spread is the degree of the scatter or the variation of the variables about a central value. Robert H. Wessel defines it as à ¢Ã¢â€š ¬Ã‹Å"measures which indicate the spread of the values are called measures of dispersion. From all these definition it is clear that dispersion measures more or less describes the spread or scattering of the individual values of a series around its central value. METHODS OF MEASURING DISPERSION: Dispersion of a series of data can be calculated by using following four widely used methods Dispersion when measured on basis of the difference between two extreme values selected from a series of data. The two well known measures are The Range The Inter-quartile Range or Quartile Deviation Dispersion when measured on basis of average deviation from some measure of central tendency. The well known measures are The Mean/average deviation The Standard Deviation and The Coefficient of variation and The Gini coefficient and the Lorenz curve All the tools are discussed in details below one after the other. THE RANGE: The range is the simplest measure of the dispersion. The range is defined as the difference between the highest value and the lowest value of the series. Range as a measure of variation is having limited applicability. It is widely used for weather forecasting by the meteorological departments. It also used in statistical quality control. Range is a good indicator to measure the fluctuations in price change like that of studying the variations in the price of shares and debentures and other related matters. Following is the procedure of calculating range: Range= value of the highest observation (H) à ¢Ã¢â€š ¬Ã¢â‚¬Å" value of the lowest observation (L) or Range = H à ¢Ã¢â€š ¬Ã¢â‚¬Å" L Advantages of Range: Range is the simplest of obtaining dispersion. It is easily understandable and can be interpreted easily. It requires fewer times to obtain the variation in the series. Disadvantages of Range: As it considers only two extreme values, hence it doesnt include all the observations of the series. It fails to tell any thing about the characteristics of a distribution It is having very limited scope of applicability Having no mathematical treatment THE INTER-QUARTILE RANGE OR QUARTILE DEVIATION: A second measure of dispersion is the inter-quartile range which takes into account the middle half i.e., 50% of the data thus, avoiding the problem of extreme values in the data. Hence it measures approximately how far from the median one must go on either side before it can be include one-half the values of the data set. Inter-quartile range can be calculated by dividing the series of observations into four parts; each part of the series contains 25 percent of the observations. The quartiles are then the highest values in each of these four parts, and the inter-quartile range is the difference between the values of the first and the third quartile. Following are the steps of calculating the inter-quartile range: Arrange the data of the series in ascending order. Calculate the first quartile which is denoted as (Q1) by using the formula In case of grouped data the first quartile (Q1) can be calculated by using the formula Where N= number of observations in the series i.e., the sum of frequencies, L = lower limit of the quartile class, p.c.f. = commutative frequency prior to the quartile class, f = frequency of the quartile class and i = class interval. Quartile class can be determined by using the formula. Calculate the third quartile which is denoted as (Q3) by using the formula in case of ungrouped data. In case of grouped data the third quartile (Q3) can be calculated by using the formula Where N= number of observations in the series i.e., the sum of frequencies, L = lower limit of the quartile class, p.c.f. = commutative frequency prior to the quartile class, f = frequency of the quartile class and i = class interval. Quartile class can be determined by using the formula. THE MEAN/AVERAGE DEVIATION: Mean/average deviation is the arithmetic mean of the difference of a series computed from any measure of central tendency i.e., either deviation from mean or median or mode. The absolute values of each observation are calculated. Clark and Schekade opine mean deviation or average deviations as the average amount of scatter of the items in a distribution from either the mean or the median, ignoring the signs of the deviations. Thus the average that is taken of scatter is an arithmetic mean, which accounts for the fact that this measure is often called as mean deviation or average deviations. Calculations of Mean Deviation in case of Discrete Series: In case of discrete series, mean deviation can be calculated through following steps The first step is to calculate the mean or median or mode of the given series Compute the deviations of the observations of the series from the calculated mean or median or mode. This deviation is also denoted as capital letter D and is always taken as mod value i.e., ignoring the plus or minus sign. Take the summation of the deviations (sum of D) and divide it by number of observations (N). In the same way one can calculate mean deviation from median or mode in case of individual series. Calculations of Mean Deviation in case of discrete series: Mean deviation can be calculated in case of discrete series in a little bit different way. Following are some steps to calculate the average mean when the series is discrete. The first step is to calculate the mean or median or mode of the given series by using the formula as discussed in the previous chapter. Compute the deviations of the observations of the series from the calculated mean or median or mode value. This deviation is also denoted as capital letter D and is always taken as mod value i.e., ignoring the plus or minus sign. Multiply the corresponding frequency with each deviation value i.e., calculate f * D. Similarly, one can calculate the mean deviation or average deviation by taking deviations from median or mode. Calculations of Mean Deviation in case of continuous series: The first step is to calculate the mean or median or mode of the given series by using the formula as discussed in the previous chapter. In the second step, get the mid values of the observations (m) Compute the deviations of the observations of the series from the calculated mean or median or mode value. This deviation is also denoted as capital letter D = m mean or median or mode and is always taken as mod value i.e., ignoring the plus or minus sign. Multiply the corresponding frequency with each deviation value i.e., calculate f * D. Take the summation i.e., (sum of D) and divide it by number of observations (N). The formula may be Advantages of mean deviation: The computation process of mean deviation is based on all the observations of the series. The value of mean deviation is less affected by the extreme items. These are three alternatives available with the researcher while calculating the mean. One can consider the mean or median or mode. Hence it is more flexible in calculation. Disadvantages of mean deviation: The practical usefulness of mean deviation is very less. Mean deviation is not having enough scope for further mathematical calculations. Mod values are considered while calculating the mean deviation. It is criticized by some experts as illogical and unsound. THE STANDARD DEVIATION: Standard deviation or other wise called as root mean square deviation is the most important and widely used measure of variation. It measures the absolute variation of a distribution. It is the right measure that highlights the spread of the observation over and around the mean value. The greater the rate of variation of observations in a series, the greater will be the value of standard deviation. A small value of standard deviation implies a high degree of homogeneity among the observations in the series. If there will be a comparison between two or more standard deviations of two or more series, than it is always advisable to choose that series as ideal one which is having small value of standard deviation. Standard deviation is always measures from the mean or average value of the series. The credit for introducing this concept in the literature goes to Karl Pearson, a famous statistician. It is denoted by the Greek letter (pronounced as sigma) Standard deviation is calculated in following three different series: Standard deviation in case of Individual series Standard deviation in case of Discrete series Standard deviation in case of Continuous series All the above conditions are discussed in detail below. a. Standard deviation in case of individual series: In case of individual series, the value of standard deviation can be calculated by using two methods. Direct method- when deviations are taken from actual mean Short-cut method- when deviations are taken from assumed mean 1. Direct method- when deviations are taken from actual mean: Following are some steps to be followed for calculating the value of standard deviation. The first step is to calculate the actual mean value of the observation In the next column calculate the deviation from each observation i.e., find out () where is the mean of the series. In the next column calculate the square value of the deviations and at the end of the column calculate the sum of the square of the deviations i.e., Divide the total value with the number of observations (N) and than square root of the value. The formula will be . Since the series is having individual observations, some times it so happens that there is no need of taking the deviations. In such a case the researcher can directly calculate the value of the standard deviation. The formula for calculating directly is . 2. Short-cut method- when deviations are taken from assumed mean: In practical uses it so happens that while calculating standard deviation by using the arithmetic mean, the mean value may be in some fractions i.e., .25 etc. This creates the real problem in calculating the value of standard deviation. For this purpose, instead of calculating standard deviation by using the above discussed arithmetic mean methods, researchers generally prefer the method of short-cut which is nothing rather calculation of standard deviation by assuming a mean value. Following are some steps that to be followed for calculating standard deviation in case of assumed mean method: The first step is to assume a value from the X values as mean. This mean value is denoted as A. In the next step deviations are to be calculated from this assumed mean as (X-A) and this value is denoted as D. At the end of the same column, the sum of D () is to be calculated. Calculate the square of each observation of D i.e., calculate. The following formula is to be used to calculate standard deviation of the series. where N is the number of observations in the series. b. Standard deviation in case of discrete series: Discrete series are the series which are having some frequencies or repetitions of observations. In case of a discrete series standard deviation is calculated by using following three methods: when deviations are taken from actual mean when deviations are taken from assumed mean Following are the detailed analysis of the above the two methods. 1. When deviations are taken from actual mean: The steps to calculate standard deviation when deviations are calculated from the actual mean are The first step is to calculate the actual mean value of the observation In the next column calculate the deviation from each observation i.e., find out () where is the mean of the series, this can be denoted as D. In the next column calculate the square value of the deviations and at the end of the column calculate the sum of the square of the deviations i.e., Multiply corresponding frequencies of each observation with the value of D2 in the next column. Divide the total value with the number of observations (N) and than square root of the value. The formula will be 2. When deviations are taken from assumed mean: The steps to calculate standard deviation when deviations are calculated from the actual mean are The first step is to assume a mean value from the observations In the next column calculate the deviation from each observation i.e., find out () where A is the mean of the series, this deviation can be denoted as D. In the next column calculate the square value of the deviations and at the end of the column calculate the sum of the square of the deviations i.e., Multiply corresponding frequencies (f) of each observation with the value of D2 in the next column. Use the following formula to calculate standard deviation c. Standard deviation in case of Continuous series: Standard deviation in case of a continuous series can be calculated by using the following steps Calculate the mid value of the series and denote it as à ¢Ã¢â€š ¬Ã‹Å"m. Assume any value from the mid values and denote it as A Deviations can be calculated from each series i.e., calculate m à ¢Ã¢â€š ¬Ã¢â‚¬Å" A and than divide it with the class interval value (i) i.e., Multiply the corresponding frequencies of each observation with the deviation value and take the sum at the end of the column i.e., calculate In the next column square the deviation values of each observation i.e., calculate Multiply the value of with its frequencies i.e., calculate Use the following formula to get standard deviation. Properties of standard deviation: As tool of variance, standard deviation is used as a good measure of interpretation of the scatteredness of observation of a series. It is a fact that in a normal distribution approximately 68 per cent of the observations of a series lies less than standard deviation away from the mean, again approximately 95.5 per cent of the items lie less than 2 standard deviation value away from the mean and in the same way 99.7 per cent of the items lie within 3 standard deviations away from the mean. Hence covers 68.27 per cent of the items in a series with normal distribution. covers 95.45 per cent of the items in a series with normal distribution and covers 99.73 per cent of the items in a series with normal distribution. Advantage of Standard Deviation: Following are some advantages of standard deviation as a measure of dispersion This is the highest used technique of dispersion. It is regarded as a very satisfactory measure of the dispersion of a series. It is capable of further mathematical calculations. Algebraic signs are not ignored while measuring the value of standard deviation of a series. It is less affected by the extreme observations of a series. The coefficients make the standard deviation very popular measure of the scatteredness of a series. Disadvantages of standard deviation: The disadvantages are It is not easy to understand the concept easily and quickly. It requires a good exercise to calculate the values of standard deviation. It gives more weight to observations which are away from the arithmetic mean. THE COEFFICIENT OF VARIATION: Another useful statistical tool for measuring dispersion of a series is coefficient of variation. The coefficient of variation is the relative measure of standard deviation which is an absolute measure of dispersion. This tool of dispersion is mostly used in case of comparing the variability two or more series of observation. While comparing, that series for which the value of the coefficient of variation is greater is said to be more variable (i.e., the observations of the series are less consistent, less uniform, less stable or less homogeneous). Hence it is always advisable to choose that series which is having less value of coefficient of variation. The value of coefficient is less implies more consistent, more uniform, more stable and of course more homogeneous. The value of coefficient of variation is always measured by using the value of standard deviation and its relative arithmetic mean. It is denoted as C.V., and is measured by using simple formula as discussed below: In practical field, researchers generally prefer to use standard deviation as a tool to measure the dispersion than that of coefficient of variance because of a numbers of reasons (researchers are advised to refer any standard statistics book to know more on coefficient of variance and its usefulness). GINI COEFFICIENT AND THE LORENZ CURVE: An illuminating manner of viewing the Gini coefficient is in terms of the Lorenz curve due to Lorenz (1905). It is generally defined on the basis of the Lorenz curve. It is popularly known as the Lorenz ratio. The most common definition of the Gini coefficient is in terms of the Lorenz diagram is the ratio of the area between the Lorenz curve and the line of equality, to the area of the triangle OBD below this line (figure-1). The Gini coefficient varies between the limits of 0 (perfect equality) and 1 (perfect inequality), and the greater the departure of the Lorenz curve from the diagonal, the larger is the value of the Gini coefficient. Various geometrical definitions of Gini coefficient discussed in the literature and useful for different purposes are examined here. CONCLUSION: The study of dispersion will enables us to know whether a series is homogeneous (where all the observations remains around the central value) or the observations is heterogeneous (there will be variations in the observations around the central value Hence it can be said that a measure of dispersion describes the spread or scattering of the individual values of a series around its central value. For this there are a numbers of methods to determine the variations as discussed in this chapter. But it is always confusing among the researchers that which method is the best among the different techniques that we have discussed? The answer to this question is very simple and says that no single average can be considered as best for all types of data series. The most important factors are the type of data available and the purpose of investigation. Critiques suggest that if a series is having more extreme values than standard deviation as technique is to be avoided. On the other hand in case of more skewed observations standard deviation may be used but mean deviation needs to be avoided where as if the series is having more gaps between two observations than quartile deviation is not an appropriate measure to be used. Similarly, standard deviation is the best technique for any purpose of data. SUMMERY: The study of dispersion will enables us to know whether a series is homogeneous (where all the observations remains around the central value) or the observations is heterogeneous (there will be variations in the observations around the central value). Dispersion when measured on basis of the difference between two extreme values selected from a series of data. The two well known measures are (i) The Range and (ii) The Inter-quartile Range. Dispersion when measured on basis of average deviation from some measure of central tendency. The well known measures are (i) The Mean/average deviation, (ii) The Standard Deviation, (iii) The Coefficient of variation and (iv) The Gini coefficient and the Lorenz curve The range is defined as the difference between the highest value and the lowest value of the series. Range as a measure of variation is having limited applicability. The inter-quartile range measures approximately how far from the median one must go on either side before it can be include one-half the values of the data set. Mean/average deviation is the arithmetic mean of the difference of a series computed from any measure of central tendency i.e., either deviation from mean or median or mode. The absolute values of each observation are calculated. A small value of standard deviation implies a high degree of homogeneity among the observations in the series. If there will be a comparison between two or more standard deviations of two or more series, than it is always advisable to choose that series as ideal one which is having small value of standard deviation. Standard deviation is always measures from the mean or average value of the series. The coefficient of variation is the relative measure of standard deviation which is an absolute measure of dispersion. This tool of dispersion is mostly used in case of comparing the variability two or more series of observation. The most common definition of the Gini coefficient is in terms of the Lorenz diagram is the ratio of the area between the Lorenz curve and the line of equality, to the area of the triangle below the equality line. IMPORTANT QUESTIONS: 1. Age of ten students in a class is considered. Find the mean and standard deviation. 19, 21, 20, 20, 23, 25, 24, 25, 22, 26 The following table derives the marks obtained in Statistics paper by 100 students in a class. Calculate the standard deviation and mean deviation. The monthly profits of 150 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean, mean deviation and standard of the distribution. The daily wage of 160 labourers working in a cotton mill in Surat cith is derived below. Calculate the range, mean deviation and standard of the distribution. Calculate the mean deviation and standard deviation of the following distribution. What do you mean by measure of dispersion? How far it helpful to a decision-maker in the process of decision making? Define measure of Dispersion? Among the various tools of dispersion which tool according to you is the best one, give suitable reason of your answer. What do you mean by measure of dispersion? Compare and contrast various tools of dispersion by pointing out their advantages and disadvantages. Discuss with example the relative merits of range, mean deviation and standard deviation as measures of dispersion. Define standard deviation? Why standard deviation is more useful than other measures of dispersion? The data derived below shows the ages of 100 students pursuing their master degree in economics. Calculate the Mean deviation and standard deviation. Following is the results of a study carried out to determine the number of mileage the marketing executives drove their cars over a 1-year period. For this 50 marketing executives are sampled. Based on the findings, calculate the range and inter-quartile range. In an enquiry of the number of days 230 patients chosen randomly stayed in a Government hospital following after operation. On the basics of observation calculate the standard deviation. Cars sold in small car segment in November 2009 at 10 Maruti Suzuki dealers in Delhi city is explained below. Compute the range, mean deviation and standard deviation of the data series. Following is the daily data on the number of persons entered through main gate in a month to institute. Calculate the range and standard deviation of the series. Calculate the range and coefficient of range of a group of students from the marks obtained in two papers as derived below: Following are marks obtained by some students in a class-test. Calculate the range and coefficient of range. By using the direct and indirect method, calculate the mean deviation by using both arithmetic mean and mode from the following data set which is related to age and numbers of residents of Vasundara apartment, Gaziabad. A local geezer manufacturer at Greater Noida has developed a new and chief variety of geezers which are meant of lower and middle income households. He carried out a survey in some apartments asking the expectations of the customers that they are ready to invest on purchase of geezer. Calculate the standard deviation of the series. Calculate median of the following distribution. From the median value calculate the mean deviation and coefficient of mean deviation. Calculate median of the following distribution. From the median value calculate the mean deviation and coefficient of mean deviation. Calculate the arithmetic average and standard deviation from the following daily data of rickshaw puller of Hyderabad City. From the students of 250 candidates the mean and standard deviations of their total marks were calculated as 60 and 17. Latter in the process of verification it is found that a score 46 was misread 64. Recalculate the correct mean and standard deviation. The wage structure paid on daily basis of two cotton factories are derived below. In order to show the inequality, draw the Lorenz curve. Total marks obtained by the students in two sections are derived below. By using the data draw a Lorenz curve. Draw the Lorenz curve of the following data. Find the range and co-efficient of range for the following data set. The height of 10 firemen working in a fire station are 165, 168, 172, 174, 175, 178, 156, 158, 160, 179 cms. Calculate the range of the series. Now let that the tallest and the shortest firemen are get transformed from the fire station. Calculate the range of the new firemen. What percentage change is found in the earlier range and the latter range? Calculate the quartile deviation from the following derived data. Calculate the interquartile range, quartile deviation and its coefficient for the following data series. Calculate the mean deviation from the following data. Calculate the mean deviation from median and mean for the following series. The distribution derived below reveals the difference in age between husband and wife in a community. Based on the data, calculate mean deviation and standard deviation. Calculate the standard deviation and mean deviation of the following distribution of workers. Calculate the standard deviation and mean deviation of the following distribution of workers. By using the Lorenz curve, compare the extent of inequalities of income distribution between mentioned two groups of persons. Calculate the standard deviation and the coefficient of variation from the following data series. calculate the mean deviation and standard deviation from the mode of the following data. Find out standard deviation from the following data. The data derived below contains the fat contents per gram of 25 chicken burgers from a fast-food shop.