Mathematically Modelling Basketball Shots Essay Example

Mathematically Modelling Basketball Shots Essay The manager of a professional basketball team is having a tough decision in choosing which of his two top scorers this season are better at free-throw shots. The final decision will go towards picking the team for Saturdays Cup Final match. On a training session one week before the match the coach decides to go all out and bring some mathematical genii in to model a situation where Lee Grimes and Dominic Aspbury, the goalscorers, will shoot at the basketball net. The mathematical genii are students from Cambridge and are benefiting from this opportunity in that they will be able to show evidence of coursework for their final exam. Their coursework will be using their abilities to collect data and test the appropriateness of a probability model on a real situation whilst the coachs aim will be to pick the better of the two players for the big game. If the random variables X and Y count the number of independent trials before the event, having a probability p, occurs then X and Y have geometric distributions: We will write a custom essay sample on Mathematically Modelling Basketball Shots specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Mathematically Modelling Basketball Shots specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Mathematically Modelling Basketball Shots specifically for you FOR ONLY $16.38 $13.9/page Hire Writer P ( X = r ) = q r 1 p where r = 1,2,3, X~G ( p ) and Y~G ( p ) I will define X as being the number of shots required before Lee shoots a basket. Therefore, Y is defined as the number of shots required before Dom shoots a basket. I will be attempting to see if X and Y have geometric distributions by taking samples of X and Y. The populations are the infinite range of shots capable from the two throwers taken in a discrete time period under varied conditions at the same level of skill. This is impossible to create so the coursework will have to involve sampling, therefore not producing results representative of the whole population. For this coursework I can not take random samples because it will not be possible to recreate due to the infinite choices of shot which could occur e.g. fatigue levels, mood type, improvement of skill level throughout the sampling etc. all could differ. I will record a sample of X by asking Lee to shoot a number of baskets and hence work out the relative frequency of success p. This result will allow me to model X as X~G ( p ) . Next I will record a sample for Y by asking Dom to shoot a number of baskets so that another value for the relative frequency of success p can be calculated. I can use the result to model Y as Y~G ( p ) . The conditions I will have to use are going to be as similar as possible to gain independent and identical shots. This will involve: * Five practice shots beforehand so that the feel of shooting is apparent a warm up before starting. * The shots being taken from the same free-throw position which is fifteen feet away from the base of the net and perpendicular to the back line. * The same type of shot being used using one hand to steady the ball and one to project the ball through the air. Same arms used each time. * The weather conditions being similar. In the sports hall there should be no significant alteration of the environment. * Each shot being taken one after the other to gain results, which will be under the most similar conditions. * When the shot is taken; a score implies one basket, a no score implies try again until you succeed. * Continue until the sample of eighty is reached and record all results If the data is successful I may be able to produce a reliable geometric model of the population from the sample enabling me to predict population parameters with greater confidence. Using the parameters I should be able to compare the populations by considering sample parameters. I have chosen a geometric model because it is an infinite distribution requiring discrete random variables and is able to accommodate the infinite range of shots that may be required to score a basket. The sum of all the probabilities will equal one (a probability density function). If X and Y have a geometric distribution, the distribution should look like this: The sample size shall be 80 as a large sample size makes the geometric distribution as accurate as possible for testing purposes. It also allows me to use the chi squared test on the model to check if there is any evidence to suggest that one thrower is better than the other at various critical levels. Assumptions that I am making to allow the model to work are that the trials are: * Identical: The factors are exactly the same. This provides a fair test and is a property of the geometric distribution. * Independent: The trials are not affected by the previous trial. The geometric model states that the events must be independent. No distribution could possibly account for the infinite amount of variables/influences that could occur e.g. improving skill as more shots are scored, fatigue etc. The variable would be different in each case. The five practice shots will make the distribution more geometric as it will warm up the performer beforehand so that they get used to the feel of shooting. * Have two outcomes score a basket or no score. * Repeated to gain the sample size Modelling the situation with a geometric distribution Let X be the number of attempts before a basket is scored for Lee: Probability of scoring a basket: P(score) = sample size/total number of shots = 80/269 = 0.2973977695 This implies X~G( 0.297 ) X can be modelled as a geometric distribution with a probability of scoring first time equal to 29.7% (1 d.p.) Finding Prob(X=r) Therefore P (no score) = 1 P (score) = 1- 0.2973977695 = 0.7026022305 Using the formula: P(X = r) = qr-1p where r = 1, 2, 3: q = probability of not scoring p = probability of scoring P( X = 2) = 0.7026022305 x 0.2939776957 = 0.2065493847 P( X = 3) = 0.7026022305(3-1) x 0.2939776957 = 0.14512205844 Finding Expected Frequency Expected Frequency for (X = r) = Prob (X=r) x sample size Therefore Expected Frequency for (X = 1) = 0.2973977695 x 80 = 23.791821 Expected Frequency for (X = 2) = 0.2065493847 x 80 = 16.7161869 Let Y be the number of attempts taken before a basket is scored for Dom: Probability of scoring a basket: P(score) = sample size/total number of shots = 80/345 = 0.231884058 This implies Y~G ( 0.232 ) Y is geometric with a probability of scoring first time equal to 0.232 (3 d.p.). This result states also that there is a 23.2% chance of scoring on the first attempt and I aim to model these results by a geometric distribution. Therefore P(no score) = 1 0.231884058 = 0.768115942 Therefore for Dom: P (Y = 2) = 0.768115942 x 0.231884058 = 0.1781138416 P (Y = 3) = 0.768115942(3-1) x 0.231884058 = 0.1368120813 Expected Frequencies will be: (Y = 1) = 0.231884058 x 80 = 18.55072464 (Y = 2) = 0.1781138416 x 80 = 14.24910733 Chi Squared Distribution The chi-squared distribution can be applied to measure the goodness of fit for the geometric models. It will examine the goodness of the model by considering the number of possible outcomes of the events and will analyse the validity of the assumptions. Thevalue will be expected to be small to suggest that the model fits the real distribution. A large value would suggest that the model is unlikely to be correct so I will use a 10% critical region to test it. * If thevalue lies within the critical region then, assuming the model is correct, it would mean that there is less then 10% chance of a result as high as this occurring. We reject the model as a consequence and conclude insufficient sampling etc. * Alternatively, if the value lies outside the critical region, the result is valid and there is a larger possibility of the value being what it is. The model is assumed to be correct and the model is accepted. Conclusion would be to state that the statistical model is appropriate to the situation and the assumptions are correct. In the tables, the expected and observed frequencies were calculated but how close together are the values? The closer the observed value to the expected value the more accurate the geometric model will be. The goodness of fit statistic is: where O = Observed Frequency E = Expected Frequency To find the best measure of goodness of fit, add up all values for each statistic and compare with the 2 probability distribution tables. The chi squared test should only be used if the expected frequency of a cell is more than five which means some of the groups are going to have to be combined. This enables the chi-squared distribution to be better approximated. The total frequency of expected frequencies should also be over 50. This makes the chi squared test work at a more accurate level. Lees chi squared test Using the equation : As we can see by the result = 7 To analyse the result with the chi squared test the number of degrees of freedom have to be established following this procedure: Degrees of Freedom = Number of Cells Number of Constraints In Lees table there are seven cells. The number of constraints is two because: o A sample size of eighty is one constraint: The sample has to be eighty. o The probability is another constraint: The mean of the model has to equal the mean of the data so we used the data to work this value out. * Therefore: Degrees of Freedom = 7 2 = 5 * at 10% critical level i.e. prob ( ) = 0.9 * but observed value of = 7.478504913 * 7.478 is less than 9.236 * therefore, the value is not in the critical region (result taken from probability distribution table) The value is not in the critical region implying the model is significant enough to use. Lees results fit into the geometric distribution model and therefore it is a good model for Lees data. There is evidence to suggest that the assumptions are true and therefore we accept the assumptions as part of the geometric model. See graph above for explanation of what the results show. Doms Chi Squared Test Using the equation : As we can see by the result = 5.694287179 * Degrees of Freedom = 8 2 = 6 * at 10% critical level i.e. prob ( ) = 0.9 * but observed value of = 5.694287179 * 5.694 is less than 10.645 * therefore, the value is not in the critical region (result taken from probability distribution table) Doms results fit into the geometric model, as the value is not in the critical region of 10%. We can assume that the geometric model was a good model to use for his results. We can again accept the assumptions as there is no evidence to suggest they do not fit into the geometric distribution. See graph above for an explanation of what the results shows. Both results are comfortably in the geometric distribution proving that they are reliable results/models and the assumptions made are valid. We can adapt Doms model so that five degrees of freedom can be used giving the same accuracy as Lees result. I am predicting that it wouldnt affect the results because there would need to be a dramatic increase in the value for it to be of any significance. Both performers have had their results analysed at the same number of degrees of freedom and there was no significant difference. It shows no alteration for the final conclusion and still no evidence is available to reject the models. Both results have shown X and Y can be modelled by the geometric distribution. By knowing this I could produce confidence intervals for any parameters I estimate from the distributions. However at this stage I will calculate the relevant parameter for this piece of coursework. I will estimate the expected number of shots required by Lee and Dom to score a basket. Expected Mean Values To find out the expected mean value for a geometric distribution it is defined as the sum to infinity of: all the probabilities, which are multiplied by the value of X (in Lees case), Y (in Doms case). This can be simplified conveniently to 1/p where p is the probability of scoring when X = 1 For Lee the expected mean value would be E[X] = = 3.3625 (4 d.p.) For Dom the expected mean value would be E[Y] = (4 d.p.) These results demonstrate the average amount of shots it takes until the performer scores. Lee, having a lower expected mean value than Dom, is shown to be the better free-thrower as he takes an average of approximately three shots to score, unlike four shown in Doms case. The total number of shots can be a very rough indicator of who seems to be the better free thrower. Lee took 269 shots and Dom accomplished 345 shots to score 80 baskets. Does this imply that Lee is more accurate? According to the expected mean values and the probabilities of scoring for each model it reinforces Lees success where all three tests are in his favour. There is a much higher chance now of Lee being picked for the game on Saturday. A factor of the investigation was whether taking constant shots at the basket improved performance. This may happen because training has occurred and the brain is learning from past mistakes. The question being asked is, were the five practice shots enough practice to enable an independent model to be produced or should it not have occurred? Raw data results were recorded in two stages; first 40 and second 40 and it suggests small decreases in many of the cells for 2nd 40 especially in Doms case. Lower values of X or Y become more frequent in the 2nd 40. This complicates results and so is a factor to consider if the coursework is completed again. The decreases in the higher X or Y values and the increases in the smaller X or Y values suggest evidence of fatigue, boredom, frustration etc. I can say now that skill level did not increase during the collection of the sample size but what is more likely to have occurred is the opposite. The explanation for Dom being more tired, bored or frustrated is probably because he shot a total of 345 baskets whereas Lee completed his in 269 shots. Two parent populations (X and Y) have been tested against geometric probability models and it so happens that they fit very snugly into them. Therefore, we can apply the knowledge that counting the amount of times before a basket is scored is modelled very well using a geometric distribution. There may be only two populations but they both show noticeable differences in their results and remain well within the statistical model. I will assume that it is highly probable for most other populations to fit into the geometric distribution on the basis that my models are very appropriate for the investigation. I have modelled the basketball situation in a real life atmosphere and the model was successful. Even though the situation is based on a theoretical distribution it was modelled appropriately. The club should now prepare for Lee having the role of free-thrower in this Saturdays cup final and accepting the fact that Dom is on the subs bench for the start of the game The data sampling was very organised and strict but not random. To have taken a random sample would mean: * Watching a random sample of club games throughout the season * Watching a sample of free-throws made by the performers from the game * Calculate who is most accurate A problem with this is time, as it would take a year to go through just one season, therefore it is impractical and illogical. The physical form of the player should also alter throughout the season so a random sample of more than one season would have to be made. A much better way is to watch all training sessions and take a general overview of who supplies the most points in miniature matches from free throws. This gives more of a view of consistency than on the day performance but during game situations the performer will be thinking more logically. A sample of eighty straight baskets is tedious and will affect performance. Modifications * Use a longer time period. The performers were rushed to collect their sample size within two hours as a result of school timetabling and so one of them had to rush his last twenty shots. * Use the same time period i.e. one performer did it one day and the other completed it the next day. Conditions may have been different and morale, energy etc may be variated for both Dom and Lee * Use foot-mats on the floor so that it indicates an exact position for the feet to stand instead of just using the line. This may be an insignificant difference but to improve the coursework it is better than no difference at all. * Using the same basketball. Half way through the sample collection the basketball was lost leaving us the trouble of having to use another basketball maybe of different weight, age etc and possibly affecting the results Improvements * I would like to calculate confidence intervals for both expected values (X and Y) to determine my degree of confidence in Lee being a better freethrower. * I would also like to be able to see if my result E[X] = E[Y] was statistically significant

Creating Two Dimensional Arrays in Ruby

Creating Two Dimensional Arrays in Ruby The following article is part of a series.  For more articles in this series, see  Cloning the Game 2048 in Ruby.  For the complete and final code,  see the gist. Now that we know how the algorithm will work, its time to think about the data this algorithm will work on. There are two main choices here: a flat array of some kind, or a two-dimensional array. Each has their advantages, but before we make a decision, we need to take something into account. DRY Puzzles A common technique in working with grid-based puzzles where you have to look for patterns like this is to write one version of the algorithm that works on the puzzle from left to right and then rotate the entire puzzle around four times. This way, the algorithm only has to be written once and it only has to work from left to right. This dramatically reduces the complexity and size of the hardest part of this project. Since well be working on the puzzle from left to right, it makes sense to have the rows represented by arrays. When making a two dimensional array in Ruby (or, more accurately, how you want it to be addressed and what the data actually means), you have to decide whether you want a stack of rows (where each row of the grid is represented by an array) or a stack of columns (where each column is an array). Since were working with rows, well choose rows. How this 2D array is rotated, well get to after we actually construct such an array. Constructing Two Dimensional Arrays The Array.new method can take an argument defining the size of the array that you want. For example, Array.new(5) will create an array of 5 nil objects. The second argument gives you a default value, so Array.new(5, 0) will give you the array [0,0,0,0,0]. So how do you create a two dimensional array? The wrong way, and the way I see people trying often is to say Array.new( 4, Array.new(4, 0) ). In other words, an array of 4 rows, each row being an array of 4 zeroes. And this appears to work at first. However, run the following code: It looks simple. Make a 4x4 array of zeroes, set the top-left element to 1. But print it and we get†¦ It set the entire first column to 1, what gives? When we made the arrays, the inner-most call to Array.new gets called first, making a single row. A single reference to this row is then duplicated 4 times to fill the outer-most array. Each row is then referencing the same array. Change one, change them all. Instead, we need to use the third way of creating an array in Ruby. Instead of passing a value to the Array.new method, we pass a block. The block is executed every time the Array.new method needs a new value. So if you were to say Array.new(5) { gets.chomp }, Ruby will stop and ask for input 5 times. So all we need to do is just create a new array inside this block. So we end up with Array.new(4) { Array.new(4,0) }. Now lets try that test case again. And it does just as youd expect. So even though Ruby doesnt have support for two-dimensional arrays, we can still do what we need. Just remember that the top-level array holds references to the sub-arrays, and each sub-array should refer to a different array of values. What this array represents is up to you. In our case, this array is laid out as rows. The first index is the row were indexing, from top to bottom. To index the top row of the puzzle, we use a[0], to index the next row down we use a[1]. To index a specific tile in the second row, we use a[1][n]. However, if we had decided on columns†¦ it would be the same thing. Ruby doesnt have any idea what were doing with this data, and since it doesnt technically support two-dimensional arrays, what were doing here is a hack. Access it only by convention and everything will hold together. Forget what the data underneath is supposed to be doing and everything can fall apart real fast.

Microsoft To Issue Record Number of Patches Essay

Microsoft To Issue Record Number of Patches - Essay Example To find the average of values in B3 and B4, a formula = (B3+B4)/2 is typed into, say cell E2, giving the4 average. Entering a value into the cell causes the value to be visible in the formula thus enabling it to be changed without edition of the formula. The easiest way to enter cell references into formulas is by typing the reference. To use values in B4 and B6 in a formula meant to calculate monthly revenue, one types in = B4+B6 then enter to get a result. However, it is much easier to utilize functions, which are algorithms that can be followed, by excel, to attain a result (Smart 5). To get the average of values in B3 and B4, one could type = then type the average function’s name, followed by a left parenthesis, then the two cells. After typing a colon, excel discerns that one is defining a cell range. On entering the cell references, one types, a right parenthesis and then presses enter to get the result. Charts display a series of numeric data in the form of a graph in order to make it easier to understand enormous quantities of data, in addition to the relationships, between the data series (Smart 7). Excel supports many chart types that help one to display data in a meaningful manner. Charts have many elements with some displayed by default, and others added when needed. The display of the elements in the chart can be changed by moving them to different chart locations, adjusting their size or reformatting them. The spreadsheet consists of a chart area, plot area, plotted data points, category (horizontal) and value (vertical) axes, chart and axes titles, and data labels. After the creation of a chart, any of its elements can be modified. One can change the chart axes’ display, add data labels and titles, add a data table or legend, and apply a special option for every type of chart. To add a chart title, one click where the title is to be added, clicks chart title on the layout tab, clicks above chart, then types the

BRAZILIAN CINEMA LAT AM 380 FINAL TAKE-HOME II Essay

BRAZILIAN CINEMA LAT AM 380 FINAL TAKE-HOME II - Essay Example Brazilian cinema prospect captured different livelihoods, beliefs and lifestyles of different groups of people, those that lived in cities or towns and those that lived in marginal areas with unfavorable conditions like the semi-arid areas where the early Portuguese first settled commonly referred to as sà ©rtao in Portuguese. Several influential renowned cinema film directors like Nelson Pereira dos Santos, Glauber Rocha, Andrucha Waddington, Jorge Furtado, Joà £o Tikomiroff, and Carlos Diegues Walter Salles amongst many others took the center stage in making these films with deeply embedded and well played out themes or motifs that clearly communicated message of importance. It is due to collective effort of these film productions developments in the 60s and 70s that led to the rise of a pro-modern movement â€Å"cinema novo†, new cinema (Rodriguez 109). that was very influential in addressing issues to do with social equality and intellectualism in Brazil as opposed to th e traditional cinema technique that were ineffective. The major themes captured by these films as portrayed in the two main settings, rural and urban, are the power in the Brazilian political landscape, religion and Brazilian popular culture. In the Brazilian context, power is closely associated with corruption in governments. The corruption in turn has led to socio-political and economical oppression to its citizens making the poor or the peasants much poorer while making the rich much wealthy creating a very big power gap between the two (Xavier 86). Power when misused is normally associated with the might or tyranny, and greed in any given society which are easily visible in the Brazilian societal and governmental structure where the rich oppress the poor because of the difference classes created and the powers that come attached. Power

CP Essay Example | Topics and Well Written Essays - 500 words

CP - Essay Example Person-centred nursing is one factor that can foster the championing of collaborative practice, but as it is evident today, it lacks in nursing due to limiting factors such as ritualistic and routine nursing. This study will suggest means of championing future person-centred interprofessional collaborative practice based on rituals/routines and person- centeredness and as the central themes. As McCormack, Dewing, and McCance (2011, n.p.) define person-centred nursing, â€Å"it is an approach to practice that is established through the formation and fostering of therapeutic relationships between all care providers, patients, and others significant to them. Orchard, Curran, and Kabene (2005, p.2) highlight organizational structuralism, power relationships, and role socialization as factors creating potential barriers to collaborative nursing. They therefore suggest that traditional routines where nurses are directed and controlled should be alternated with supportive environments. In short, nurses should be able to air their views, consult with patients, and be part of the decision-making bodies (Hall &Roussel 2012, p.154). On matters of power imbalances, teamwork should be supported by scraping the organizational cultures where rather than work as teams, health professionals identify with their â€Å"common† groups and this clogs their ability to consider the per spectives and opinions of others (Reeves, Lewin, Espin, &Zwarenstein 2011, p.89). This not only affects the professionals, but the patients and the organization at large. In addressing this, collaboration should be instilled within healthcare contexts by shifting focus on cooperation rather than on competition as nursing is defined as a practice based on discipline (Black 2013, p.63). Therefore, nurses should realize that their focus is more on patient wellbeing than their own personal gains. Collaborative nursing practice, again, can be through creating an understanding

A view on cumulative satisfaction

A view on cumulative satisfaction Whether in doing business or as an end user of a product or service we tend to realise the importance of value for money. Consumers look for products or services of good quality for the price that they are willing to pay. This pursuit of value is the basis of their perceived satisfaction. Customer satisfaction plays a vital role in deciding value. The overall purpose of this article is to identify the importance of customer satisfaction for organizations and most essentially when and why cumulative satisfaction is important for businesses today. It is vital to make sure that the customers are happy and to view customer satisfaction as a main key to organisational success. Quality of a product or service is a means to an end. Customers perception of a products quality is part of a customers assessment of value and satisfaction. What is Customer Satisfaction? In todays competitive business environment, Organisations thrive to become the market leaders in their respective fields to gain profits. Customer satisfaction is seen as the key to any companys competitive advantage and profitability. It is the overall customer attitude towards a product or a service provider, or the reaction to the difference between what the consumer expects and what they receive, in order to fulfil a need or desire. Customer satisfaction is a highly personal assessment that is affected by customer expectations and is also based on the customers experience with a service or a product, idea, personnel. Imagine going to a reputable shopping venue in Sri Lanka such as Odel, where the atmosphere is excellent for shopping. Renowned for quality products ranging from clothes to jewellery and also provides various facilities such as handy ATMs, telecommunication, cafes where customers can sit and relax after shopping, the play area for children with adult supervision, and the efficient staff who are willing to help all their customers with a smile. In such a place, the overall experience that a consumer gains is what creates value for customers. This value creation adds to the overall satisfaction of the customer. The atmosphere at Odel and the quality products along with the services would affect the customer satisfaction. Customer satisfaction and its effect on Organizational profitability Businesses focus on Customer satisfaction mainly to increase their customer loyalty; this generates repeat purchases, thereby increasing their revenue, and importantly helps them to survive among the intense competition. Exemplary organisations focus on how to give their customers a positive experience in order to gain their trust and loyalty because the purchasing behaviour of loyal customers creates higher organisational revenue and reduces the cost of doing business. Satisfied customers will often refer the business to their family and friends which will create positive word of mouth, attract new customers and minimise the costs of advertising. When customers are highly satisfied they are less likely to switch to other service providers. For example a loyal customer of HSBC who is been given recognition for being a HSBC card holder for a long period will be treated exceptionally by the bank, providing him with premium rates, special bonus packages, and therefore this satisfied customer will not want to switch to another bank. Although attracting new customers is important it also can be costly, but serving current customers who are well satisfied with the business and its service can be rather cost efficient. Moreover, highly satisfied customers are less price-conscious because they are brand loyal and will pay a premium price for a product or service. Therefore having satisfied loyal customers will most certainly have a direct impact on profit. This is why successful businesses focus on customer satisfaction. Change in the perception of customer satisfaction through time There was a time when customers were less demanding and less vocal if they were less satisfied with a product or service. This is not that time. In the modern business context customers are becoming more demanding and less tolerant and with a combined increase in expectations, they are ever more concerned with their satisfaction and look for recognition and respect from these service providers. Customers have more power and therefore demand much more than just the product or service. Today, customers are looking for that extra value added full package as opposed to just the product or service. It is the basis of their customer satisfaction. So when is customer satisfaction most important for businesses? The answer is now. It has never been more vital. Cumulative satisfaction and its impact on business Overall satisfaction is not based on a single experience, but rather a chain of positive experiences bringing about a cumulative sense of satisfaction. The perceived value at the pre-purchase stage is short lived, however it sometimes transforms into satisfaction in the post-purchase stage. This post-purchase satisfaction results in repurchases and leads to greater trust and customer loyalty which is a result of cumulative customer satisfaction. A product has five key components such as goods, services, experiences, ideas, and people. Quality should be embedded in all of these components which ultimately creates value, when what is been received is evaluated against what is been offered leading to transactional satisfaction or results of one off exchanges. If a consumer is satisfied with a particular experience, that will eventually lead to cumulative satisfaction where the consumer engages in multiple experiences. Cumulative satisfaction is a psychological state, which leads to a deep sense of trust towards the product or service. This trust will be embedded in the customers mind and therefore will not think twice about purchasing the product or service. For instance, when a customer goes into a groceries super market such as Cargills food city, they reach first for the reputed brands in which they lay their trust. For instance if a customer has been using Colgate toothpaste for the past five years and trusts the brand through experience, thereby he will undeniably select and purchase that particular brand among many other toothpaste brands. This unconscious loyalty stems from countless positive experiences associated with the particular brand. This is what most businesses are looking for. Cumulative satisfaction; as the basis of customer relations In an increasingly impersonal world, customers look for personalized service. Since customer satisfaction varies depending on the individual, it is essential that businesses tailor their services for the customers subjective needs. This is where building customer relationships begin. Since cumulative customer satisfaction leads to loyalty and trust, it is plausible to state that customer relations stems from customer satisfaction. Giving a one-on-one service will enhance the customer experience providing greater cumulative satisfaction. Customers therefore will revisit the business and thus strengthen the relationship between the customer and business. For instance consider salon, Ramani. It is a reputed and leading salon in Colombo. They pay attention to detail, whiles giving an additional touch to the whole salon experience by providing not only a tranquil environment but also a calming beverage. Most importantly, they give a tailored service to each customer. Therefore a relationship is built between the customer and their stylist. This is further strengthened through regular visits and revisits. It is clear that customer relations are rooted by cumulative satisfaction. Due to years of experience and satisfaction, a relationship is built between the customer and her stylist. Furthermore, it should be noted that any decision made to remain loyal to the product or service or move to a competitor is based on prior experience and is positively correlated with the duration of the relationship throughout which the customer has been satisfied. Therefore businesses should consider the longer the relationship between the customer and service provider, the less probability of losing that customer to a rival business. Ways that businesses can improve customer relations In order to improve the cumulative satisfaction levels of customers, service providers should continue to aim at delivering good quality services and products in order to improve the total product value and to build profitable relationships based on cumulative satisfaction. Keeping the consumer happy should be their main goal, to retain the customers loyal and satisfied, businesses should delight their customers and give due recognition to their loyalty, for instance profitable customers should be given special treatment such as special bonuses, loyalty cards, special discounts. Some service providers go to the extent of keeping track of their customers birthdays and send cards for these special occasions, this is in order to maintain a healthy relationship with their customer base. The famous Ritz-Carlton hotel keeps a record of all their guests favourite snack, chocolate, which is entered into a computerized tracking system so that when the guest returns to any of their worldwide hotels these items, will be offered to the guest to make them feel special. Creating cumulative satisfaction does not always have to be done in a huge scale but making the customers feel special while providing value for their money is what should be done, giving customised products and service, having good and efficient employees to fulfil every customers needs, anticipate their needs before the competitors take action, asking customers about their needs, getting feedback in order to avoid any defects.. As small and medium organisations, you should keep in mind how cumulative satisfaction can lead to Organisational success and profitability. It is of paramount importance to build and maintain relationships with your consumers that will eventually lead to customer loyalty and trust.

The Island of Aruba :: Free Descriptive Essay About A Place

The Island of Aruba From Aruba’s discovery at the end of the thirteenth century to present-day, its history is filled with change. Its changing possession and the three economic booms that it experienced form the outline of thousands of years. The changes the island has gone through are truly remarkable, and it is unbelievable that the island that now seems to be saturated with tourism was once a desolate landscape with little agricultural promise and economic hope. Unfortunately Aruba’s history is lacking documentation, but it is undisputable that even before the island was claimed, there were inhabitants on the island that would soon be considered the first chapter of Aruba’s history. There is no written historical documentation that states who discovered Aruba, but it is believed that a Spaniard named Alonso de Ojeda was the first European explorer to land on the island in 1499. He initially thought that he had found an â€Å"island of giants† because the remains that he discovered seemed to be larger than that of an average European. It can be speculated that the name Aruba is derived from a Spanish phrase â€Å"oro huba† or in English â€Å"there was Gold†. The Spanish, however, thought that the land was â€Å"valueless† because they did not discover any underground geological worth. It seems strange, though, if the name came from this Spanish phrase that they would have counted it among the â€Å"valueless islands.† There are two other suppositions that seem more plausible. The Carib language of the Antilles, which was passed on by the missionaries, the French Dominicans Breton, Labat, Du Tertre, supports the derivations ora (shell) and oubao (island), which would together mean â€Å"shell-island†. Some people have also suggested the name comes from words meaning companion or guide. There is no way to be sure, and any attempt to uncover its true derivations would be guesswork. It is not known when the first human beings set foot ashore, but considering that natural resources were poor, it is likely that the island acted as nothing more than a halting-place for a succession of tribes and clans. Long before the Spanish claimed the land, maybe even as long as 4,000 years ago, it is believed that the Caquetio Indians of the Arawak tribe came to the Aruba to seek out a safer place to inhabit. They had previously lived on the Paraguana peninsula in Venezuela but were forced to leave because of continuous threats by the Carib Indians.

Compare and contrasts of ‘The Soldier’ by Rupert Brooke and ‘Dulce et Decorum est’ Wilfred Owen Essay

Wilfred Owen and Rupert Brooke both share the similar themes within their poems, which are war and death. Although there is unconformity within their views due to their backgrounds and experiences. Brooke was very idealistic, which makes sense when he never actually got to fight in the war as he died shortly before where as Owen went through the genuine experience. Two poems that highlight these two contrasts are ‘The Solider’ and ‘Dulce et Decorum est’. In ‘The Solider’, Rupert Brooke illustrates how a soldier is reflecting on the possible death going away to war may bring. Although from his opinion his death if so was to happen shouldn’t be mourned and his death will be a tribute to his England. When compared to Wilfred Owen’s ‘Dulce et Decorum est’ the views are far from similar. Brooke states dying for your country is honourable where as Owen interprets dying for your country is not all glory and honour and more pain and suffering. Both poets desire different forms to present their poems. ‘The Solider’ is a sonnet which suits Brookes type of poems as he romantises the theme of war ‘The Solider’ is very much as well a love poem to his idealized England. Where as Owen opts for the more simple 8. 8. 11, Owen doesn’t seem to have a solid form as Brookes does. They both share the rhyming pattern of ABABCDCD which allow their poems to flow and create rhythm. The structure ‘Dulce et Decorum est’ can be broken down into three parts, an outsiders description and recollection of events featuring soldiers withdrawing from the frontline, a man within the battle himself, and a addressing to the reader of confrontation to those who share the idealistic view of war. Owens poem creates a build up towards his main point in which he finishes off with ‘The Old lie; Dulce et Decorum est Pro Patria mori’. From Owens experiences ‘Dulce et Decorum est’ acts as a warning and a hit of realism to those who are at home. ‘The Solider’ is a much more relaxed peaceful sonnet. Brookes use of natural imagery creates a more calm aspect of war. ‘Dulce et Decorum est’ features intense imagery as the key of Owens poem is to get across a point of the horrendousness of war. Within ‘The Solider’ Brooke recalls the memoirs of a fallen solider whom declares his patiotism to England by declaring that his death shall be the eternal ownership of England, of a small portion of land he has died upon, Brooke doesn’t have a main structure to his poem as his point is connoted though out the whole of the sonnet. This sonnet canbe split into two stanzas, the first stanza refers to the physical part of the solider and the second a more psychological point of view. Within the physical part the words used refer to things that can physically be touch ‘bore’ ‘shaped’ ‘made’ in the second is more things you cant touch ‘mind ‘thoughts ’ ‘sounds’ ‘dreams’. Both poets use different types of language to get across their ideas. ‘Dulce et Decorum est’ uses harsh and meaningful language. His uses of metaphors creates deeper impact and imagery ‘blood shod’. Owens opening stanza has caracterism of the language about ‘fatigue’, they ‘limped on’, ‘marched asleep’ this connotes pitiful language which intends to reveal the reality of war. Alliteration is used to reflect the agonising of the gas victim ‘And watch the white eyes writhing in his face’. Owen features a shift of register which grabs the readers attention ‘Gas! Gas! Quick, boys!’ this change of register adds more realism and switches the point of view to a soliders. Rupert Brooke uses personification to the word ‘England’, ‘gives somewhere back the thoughts by England given’. Brooke uses pure language within his sonnet such as ‘gentleness’ ‘heaven’ love’ ‘blest’.

Aztecs and Native Americans essays

Aztecs and Native Americans essays Two of the biggest and greatest civilization in the Americas were the Aztecs and Incas. These two civilization were both said to be conquered by the Spanish, but it wasnt just the Spanish who conquered them. These two civilizations both fell from a combination of a weak government, lack of technology, new disease introduced by the invaders, and not being prepared for the For many centuries the Aztec civilization revolved around a ideological, social, and political system in which expansion was the cornerstone. Expansion was the cornerstone of their whole civilization, because their religion requested that a large number of human sacrifices where to be made to the gods. To get the sacrifices the Aztec went to war with other tribes in Mexico to get these human sacrifices (Conrad conquest more sacrifices and more land was added to the Aztec kingdom. The Aztec were a strong civilization who were familiar with organized large scale war, had specialized war chiefs, and a well organized system of territorial levy in which large armies could be amassed in a short time (Age of Reconnaissance 124-125). They may have been well organized for war, but they were not prepared for internal changes in there civilization. When expansion was no longer an option there system crumbled. Without expansion they could no longer give human sacrifices in the same amount in which they use too. Upon the arrival of the Spanish the Aztec government was falling apart, and "Moctezuma II programs of internal military consolidation and administrative and social stabilization had failed" (Conrad s first met the Spanish they were amazed by them. The Spanish used the Aztecs own legends to take advantage of them and gain the upper hand. Other disadvantages that the Aztecs had was the need to take prisoner to sacrifice, they were not untied with...

Thomas Mathus Principles of Population Essays

Thomas Mathus Principles of Population Essays Thomas Mathus Principles of Population Essay Thomas Mathus Principles of Population Essay Thomas Malthus Principles of Population Today, there is both agreement and disagreement of Thomas Malthus’ essay on the principles of population. Malthus stated that population grows exponentially or at â€Å"geometric rate† and food production grows at arithmetic rate, or linearly. Geometric rate grows in a series of numbers (2,4,8,16,32†¦etc. ), which shows that children will grow up and each have their own children, and those children will have their own children. Eventually the base numbers of children will be so high that the population will grow rapidly, out pacing food production. Food production grows arithmetically in a series of number (2,3,4,5,6†¦etc. ) Today, some geographers believe that Malthus’ theory can be used to predict future population issues. The demographic transistion theory gives some explaination behind each side of malthus’ theory. The demographic transition theoy is shown through different stages of growth. Stage 1,low growth (high birth and high death rates),stage 2,high growth (high birth and low death rates), stage 3,moderate growth(low birth and low death rates), and stage 4, low growth(low birth and steady death). Countries that are in stages 2 and 3 are growing rapidly, without a fast food production. For example, in lesser developed countries such as Nigeria the population is growing rapidly, and out pacing the production of food. Also, with today’s medical technology, people are also living longer. The longer someone lives, the more food they need to stay alive. Some geographers are against Thomas Malthus’ theory on the principles of population. Although people are living longer, with a growing population also comes advancement in food technologies. Thomas Malthus did not take the advancements in the food technology into account when he proposed this theory. New food production advancements include technologies such as chemical fertilization, so more food is able to be produced. In countries that are in stage 3 and 4 of the demographic transition theory, such as the United States, there is a slow population growth. Additionally, there are many new technologies in food production and an abundant supply of food offered to United States citizens. This is an example of a place where the food production can keep up with the population growth.

Types of Marketing Strategies and Elements of a Successful Marketing Term Paper

Types of Marketing Strategies and Elements of a Successful Marketing Strategy - Term Paper Example One should remember that marketing is not like mathematics, in which there are set formulae to derive results. However, goals are met on the basis of past experiences, and some trial and error. Marketing strategies are based on the principles of psychology and sociology and believes in one core value that customers come first; therefore, one needs to satisfy their needs. TYPES OF MARKETING STRATEGIES Marketing strategies are divided on the basis of the status of the organization in the market, its stage in the life cycle and also on the basis of different levels in the company. Strategies based on Market Dominance Market Leader Strategies Market leader focuses on expanding total market, defending market share or expanding market share. Total market can be expanded either by attracting new users, creating more usage or new usage. Market share can be defended through â€Å"position defense, flanking defense, pre-emptive defense, counter-offensive defence, mobile defence, market broade ning, and market diversification and contraction defense† (Smith, n.d). Market Challenger Strategies A challenger can attack the leader by making â€Å"a frontal, flank, encirclement, and bypass or guerrilla attack† (Smith, n.d). Other strategies available to a market challenges include â€Å"offering price discounts, offering goods at low cost, introducing prestige goods, doing product proliferation, bringing innovation in the product, improving services, bringing innovation in the distribution, reducing manufacturing cost or doing intensive advertising† (Ranchhod, Tinson, & Gauzente, Marketing Strategies, 2004, p. 182). Market Follower Strategies Market follower can either become a counterfeiter, cloner, Imitator, or adapter. Market Niche Strategies Market niche follows â€Å"market differentiation strategy† (McDonald, 1995, p. 50). Porter’s Generic Strategies Porter generalised marketing strategies in three broad types that companies can choose f rom in order to get a competitive advantage. These are â€Å"market segmentation, market differentiation and cost leadership† (Bradley, 2005, p. 152).  

Emergency Response Plan MOD 1 SLP Essay Example | Topics and Well Written Essays - 500 words

Emergency Response Plan MOD 1 SLP - Essay Example All these are hot sports for fires and disasters and hence mitigation plans to prevent such disasters as well as plan on emergency response in case the fire disaster happens should be in the plan. California as a whole including this county is a very hot area and hence fires are likely to happen and when they do they are likely to spread faster and wider in a short period of time (White, T., Ariaratnam and Michael, 2012). Riverside County has been reported to have several hundred earthquakes and earth tremors this year alone. This therefore means that the area is liable to earthquake disasters of larger magnitude and the emergency response team should be prepared on ways to handle it. Earthquake is a natural disaster and hence there are no mitigation efforts and preparations that can be made. The only way to tackle such a disaster is to wait for it to occur so that rescue efforts can be put in place. Even though the area has never experienced an earthquake of higher magnitude to crippling and alarming levels according to richer scale, this does not mean that it should be ruled out as a disaster possibility. California is generally an area prone to earthquakes and even if the earthquake will not happen with the Riverside County, the effects of a huge earthquake can be passed to this county and hence strong response is necessary (Geschwind, 2001). Terrorism is a man-made emergency and disaster that is likely to happen in Riverside County similarly to any other place in the US what with the terrorism threats and activities already taking place in other locations in the country. This county is likely to be a target because of several reasons first being the fact that it has a military base known as March Air Reserve Base. The military has been an enemy of terrorists and hence are likely to attack the county as a way of retaliation. There is also an international airport where they can arrive from which is the Palm Springs International Airport.