Risk and uncertainty Essay Example | Topics and Well Written Essays - 500 words

Risk and uncertainty - Essay Example In contrast, there is an uncertainty when individuals are not informed of the outcome or of its distribution. Some authors suggest that risk is about the outcome of events whereas the uncertainty is specifically related to its probability. An effective inventory management is essential to ensure the better use of inventory. If the prevailing economic and market conditions are favourable, the organisation may use the inventory at its best level to generate more profits. Likewise, the firm should not choose to use inventory on a large scale when the existing business conditions are not promising. Businesses should use their excess capacity once they identify an emerging opportunity to expand their market territory or to increase sales volume. For instance, firms may use their excess capacity in peak seasons to take advantages of the favourable market situation. A cake manufacturing company must use its excess capacity in festival seasons like Christmas, New Year, and Easter because there will be an increase in the market demand of cake during these seasons. By using the excess capacity, the company can improve its production capacity to meet the increased supply needs. In addition, a company can use its excess capacity when demand conditions are favourable. To illustrate, a company would experience increased demand for its products/services following a positive review by reputed agencies and therefore the company must increase its capacity to benefit from this particular business situation. A number of strategies can be used to minimise risk/uncertainty exposure during the product launch (Harley Davidson low-to-the-ground hover bikes). It is clear that the organisation would not be informed of many risks and uncertainties when it launches the product into the market. A prior market survey can really assist the organisation to minimise its risk/uncertainty exposure to a great extent. The business can make use of the wide popularity of the social

Movie ticket pricing Essay Example for Free

Movie ticket pricing Essay Household behavior forms an interesting area of study for economists given that the human aspect involved in making of economic decisions by a household vary a lot depending on the perception of a commodity or service in the market. This is done in the view of gaining a certain level of utility only known to the consumer. One such area that has attracted scrutiny is the consumption and pricing of movie tickets and goods sold in the movie theaters. An article by Jennifer McNulty titled â€Å"Concessions on Movie Ticket Pricing? details the tricks present in the pricing of movie tickets and products such as popcorn crisps and soft drinks sold in the movie theaters. This paper critically analyses this article and discusses the economic sense in the article plus a reflection on the whole issue. Article review In this article the writer is worried about the high charges of popcorn in movie theaters than in ordinary shopping outlets. This she poses as the introductory question in the article asking â€Å"why does popcorn cost so much at the movies? † She notes that despite the high prices, movie goers are always willing to pay the high prices charged for the popcorn as evidenced by â€Å"all the people standing in line waiting to buy popcorn, soft drinks, and candy†. The author notifies us of the findings of a research by Stanford and the University of California, Santa Cruz that reveals the trick behind this idea. The findings show that charging lower prices for primary products in this case movie tickets and charging higher prices for secondary products in this case popcorn, beverages, peanuts etc drives the customer into seeing the bargain in the primary product and not the overcharging in the secondary product. This will always keep demand for both high courtesy of low price tickets. The author says â€Å"If you want to bring more consumers into the market, you need to keep ticket prices lower to attract them†. Products sold in movie theaters are charged on concession basis in that there is an added price on the product as a â€Å"commission† to the vendor. They account a lot in term of revenue for movie theaters as Jennifer says that â€Å"movie exhibition houses rely on concession sales to keep their businesses viable†. The idea according to Jennifer is that movie theaters transfer some movie charges to the concession goods. This then increases demand for movie tickets and revenues high but profits low. From the article we see that â€Å"Although concessions account for only about 20 percent of gross revenues, they represent some 40 percent of theaters profits†. Therefore it would seem that it is better to charge low prices for tickets so as movie consumers are made to believe that they have â€Å"saved† some amount on which they can spend on the concession goods. Unfortunately, this is just an illusion as the moviegoer ends spending more. Economic analysis of the article The movie theaters have hinged their business sense on the demand elasticity in response to price changes. They have noted that a proportionate increase in the price of movie tickets leads to a more than proportionate drop in demand of movie tickets. Therefore we would say that demand for movie tickets is perfectly elastic to price changes. On the other hand, demand for concession goods is not affected, as per the article by change in prices thus perfectly inelastic. Nevertheless, we would normally expect perfect some degree of elasticity when prices are increased to inconsiderate levels. This would probably force moviegoers to carry along products that they could have otherwise bought at the theater. From another economic perspective, we can say that there is a level of complementarity between the movie tickets and the concession goods though it is one sided. This is because of the fact that concession goods will and can only be consumed after purchasing a movie ticket. However, one can consume a purchase/consume a movie ticket without necessarily having to purchase any of the concession goods on sale in the theater. For fully complementary goods, it is impossible to consume one good in the absence of the other. In such cases, the price and demand of one affects the other. In the case of movie tickets and concession goods, the demand for movie tickets leads to a considerable increase in the demand for the more profitable concession goods. Unfortunately, demand for concession goods does not in any way affect the demand for movie tickets as a consumer can make use of the movie ticket alone without the concession good. Reflection Consumption of leisure hours by households do not usually follow economic principles witnessed in other goods and services. Households attach levels of utility on leisure hours as determined by fashion trends and culture. The idea of purchasing and consuming goods such as popcorns and peanuts in the movie theaters is something that has been nurtured by today’s generation and fashion. This is what is demonstrated in the article in that there is no economic sense that can link any complementing aspect between concession goods and movie tickets but just a creation of our society. It is thus the movie theaters that have capitalized on this fallacy to gain profits. I would personally think that the movie theaters have succeeded in making the best use an economic opportunity and are creating and inducing demand for otherwise low selling products in the name of concession goods. Therefore, the article plays its purpose of informing the moviegoers of where they â€Å"cheated†. In economic sense, the paper shows the power of elasticity in action.

Gay, Lesbian and Bisexual Issues - Michael Levin vs. Richard Mohr :: Argumentative Persuasive Essays

Homosexuality - Michael Levin vs. Richard Mohr Homosexuality has been on debate for numerous years. It is mentioned in the Bible which is thousands of years old. But recently two philosophers have spoken how they feel about Homosexuality. Michael Levin and Richard Mohr's views on the subject are in conflict with one another. Levin argues that homosexuality is abnormal because it is a misuse of body parts that have evolved for use in heterosexual intercourse (Levin 354). Furthermore, because natural selection has made the exercise of heterosexuality rewarding to human beings, homosexuality has a high probability to unhappiness. Mohr refutes Levin's stance about homosexuality myths and stereotypes. He rejects arguments that homosexuality is immoral or unnatural. Levin exemplifies the point that homosexuality is misuse of body parts with the case of Mr. Smith, who likes to play "Old MacDonald" on his teeth so devoted is he to this amusement, in fact, that he never uses his teeth for chewing but instead takes nourishment intravenously. This is a clear example where Mr. Smith is misusing his teeth. In addition to misuse, Levine states that this man will have a dim future on purely physiological grounds (Levin 355). Since Mr. Smith isn't using his teeth for chewing, his digestive system will suffer from disuse. The result will be Mr. Smiths deteriorating health. Levin incorporates the evolution process into this example. He states that Mr. Smith descended from creatures who enjoy the use of such parts. Creatures who do not enjoy using such parts of their bodies will tend to be selected out. In particular, human males who enjoyed inserting their penises into each other's anuses have left no descendants. Homosexuality is likely to cause unhappiness because it leaves unfulfilled an innate and innately rewarding desire (Levin 355). Mohr takes a completely different stance on homosexuality. According to Mohr, homosexuality is perfectly unobjectionable. The unnaturalness charge that Levin give homosexuality carries a high emotional feeling. This feeling is usually expressing disgust and evincing queasiness. An example of such feelings are some people's response to women who do not shave body hair. Many of the people who have a strong emotional reaction, without being able to give good reasons for them, we think of them not as operating morally, but rather as being obsessed and maniac (Mohr 367). So the feelings of disgust that some people have to gays will hardly ground a charge of immorality. The idea of "natural" is a key defense in Mohr's debate. He states that natural is that it fulfills some function in nature. According to Levin, homosexuality on this view is unnatural because it violates the function of

Alfred Hitchcock has been called ‘the Master of Suspense’, considering ‘psycho’ state how effectively he achieves the element of suspense in this film

Alfred Hitchcock has been called ‘the Master of Suspense', considering ‘psycho' state how effectively he achieves the element of suspense in this film. The film Pycho is known for its suspense. The dictionary definition of suspense is ‘the anxious uncertainty the audience feels while waiting for an event. It's an attraction/repulsion response, or that ‘oooooh errrrr' feeling! ‘ I personally think that suspense is the feeling of not knowing what's about to happen, feeling unsure of how to react to the next thing that happens. It puts you in to a state uncertainty or excitement, like you are waiting for a decision. It makes you feel a degree of apprehension or anxiety. Alfred Hitchcock was brought up in a strict Roman Catholic environment. He always knew exactly what was right and what was wrong and was aware of other people's wrong doings. This comes across in the film. Marion was the first woman to be murdered and she was also the first person to be seen as immoral, she was seen in white underwear in the first scene as she was in bed with a man she was having an affair with. This shows her flaunting her sexuality. She was also seen flushing the toilet just before she was murdered. This is another thing that Hitchcock was brought up to think was immoral also Hitchcock was a misogynist. This might explain why he killed off the main female character in the film. Work played a huge part in Hitchcock's life, he was a workaholic infact. People would describe Hitchcock as obsessive with his films because he would devote his life to and take so much pride in them. Psycho was released in 1960. The morals and attitudes of people were a lot different in 1960 to what they are now. There were far more of the population who attended church and would call themselves ‘christian'. Also there was a much surer sense of definite rights and wrongs; moral and immoral behaviour was much more clearly defined. In the film this comes through clearly. In 1960, men were thought to be superior to woman they certainly occupied the higher status in their occupations. Marion is at work and the man who has come in to speak with her boss is talking to her. He looks old and arrogant. He is boasting about how rich he is, telling Marion about how he is buying a house for his daughter. He is trying to chat up Marion but she ignores him. He sits on her desk so that he is at a higher level than her to show that he is more important. Marion is seen in her underwear. This was a very rare thing to see in any film in 1960. Before she stole the money she was seen in white underwear which is shocking enough. After she has stolen the money, she is seen again in her underwear but this time it is black. White is seen as a pure colour so this is why she was wearing white before she stole the money where as black is not pure, a dirty colour, this is why she was wearing black after she had stolen the money, to symbolise that she has become immoral. The audience can now expect something bad to happen. Just before Marion steps into the shower were she gets murdered she flushes a check down the toilet. Films would never show a toilet being flushed in 1960. It was looked up on as an immoral thing to be seen. Now, in 2003, seeing someone flush a toilet on a film is completely normal. The film starts with a shot of Marion and Sam (her secret boyfriend) in bed. They talk about running away and getting married. Marion goes into work that day as if everything is normal. She sits down at her desk when her boss walks in with a man. The man sits down on her desk and starts telling Marion about the $40000 he has in cash to buy a house and he gives Marion the $40000 to put in the bank but Marion steals the money so that she can get married. She drives to a motel – the ‘Bates Motel', and gets herself a room. She spends sometime talking with Norman Bates, the owner, and then goes to her room for a shower but as she has a shower someone murders her. Norman then takes Marion's body and puts it in a river. Marion's sister, Lila, realises she is missing and asks Sam if he knows where she is, he doesn't. Arbogast is a detective who try's to find Marion so he goes to the motel to see if she is there but Norman says that he doesn't remember her. Arbogast still suspects something so he goes to Norman's house however as he goes up the stairs, he also gets murdered. Sam and Lila realise that Arbogast hasn't returned so Sam goes to the motel to look for him but he can't find him so then Sam and Lila go back to the motel. Marion's sister goes into the house to look for Norman's mother as Sam and Lila think that she knows something. Lila goes down to the cellar and finds a skeleton of Norman's mother just as Norman comes in to the cellar dressed as his mother with a knife to kill Lila but Sam stops him. Norman's mother was dead but he believed she was still alive, for example, he would pretend to be her and it was Norman being his mother who had murdered Arbogast and Marion. This is a horror/thriller film. It focuses on an individual who is mentally ill and it explores some of the possible consiqueses of mental illness. This is one of the most successful of Hitchcock films. This could be due to the amount of suspense in it. Hitchcock has used very successful techniques of creating suspense. There are many scenes in Psycho that are suspenseful for example the shower scene where editing was used in a bold and sharp way. The shower scene, in which Marion was brutally murdered, was a huge hit with its audiences. This is because is was so suspenseful. The quick cuts – the entire stabbing lasted only twenty seconds, the sound effects – you could hear the tearing of the flesh as the knife broke the skin but you never actually saw the knife cut the skin, the music – all strings, very high pitched, the sort of music that makes you cringe and know that something big is about to happen, all created a great amount of suspense. When Marion is in the shower we see the door of the bathroom open, but Marion doesn't. Seeing this makes us pay attention, at this point the suspense starts. Then the music starts and we see the knife. At this point we are almost certain that she is going to be murdered. Then the murderer pulls back the curtain and Marion screams. In my opinion, this is the most suspenseful point in the murder. As she is being stabbed, there are alternate shots of Marion and the knife and the music is very loud and fast. When the murderer has gone, everything slows down as Marion slides down the wall and falls to the ground. There is a close up on the blood going down the plug hole after the camera has very slowly zoomed in on it. There is then a close up on Marion's eye, as she lies dead on the ground, and the music is very low and slow and then all the action is over and the level of suspense suddenly drops. This plays with the mood of the audience, it takes them from a state of tension or anticipation, building up to the point were the murder is commited and then giving the audience a kind of release. The music plays a big part in creating suspense. The music used in Psycho is very sinister, high pitched and high tempo. The music not only creates suspense, it adds a certain amount of tension. As the camera focuses on different things, the music tempo and pitch changed to build suspense, for example, as the camera pans across the room with the money in it the music is a medium tempo but as the camera zooms in on the money the tempo of the music shoots up. This draws your attention to the money. Another of the most suspenseful scenes in Psycho is where Arbogast is murdered. He walks in to the house slowly and curiosly. This is suspenseful as the audience know he's looking for something and are waiting to see what it is. As he walks up the stairs, the audience see a door open slowly. This builds the tension and anxiety that the audience feel. We see someone step out of the room, at this point the music that was heard when Marion was murdered was played. The audience now associate this music with murder. The person who stepped out of the room starts to walk quickly over to Arbogast on the stairs. The music is very loud and quick at this point. The audience's heart rate is automatically increased and they are more exited/uncertain. You then again hear him being stabbed but don't actually see it. As Arbogast falls down the stairs, the camera is above him, and he then falls to the floor and the murderer stabs him again, then the music suddenly stops and the camera cuts straight to a different scene. All through that scene there is a lot of suspense. There is a great deal of suspense created in the scene where Lila goes to talk to Norman's mother. Lila walks down to the cellar. The audience thinks she is down there because Norman had said previously that he was taking her down there. When Lila walks into the cellar, she sees the back of who she thinks is Norman's mother. She turns Norman's mother around and find only the skeleton of her. Throughout this scene there is slow low music playing until she sees the skeleton then the music speeds up. We then see Norman running in to the cellar dressed as a woman. This confuses the audience but builds the suspense as the audience are unsure. When Norman walks into the cellar the music changes to the music played for the previous two murders. The music automaticly creates suspense as the audience presume there will be another murder. At this point, the audience immediately suspect that he is going to murder Marion's sister but then we see Sam who stops him from murdering her. This creates suspense because it is a twist to what has happened with the other murders, so we do not know what to expect. As Sam fights with Norman he knocks the light bulb so it is swaying. There is a close up of the skeleton, it is in the shadow, then in the light, then in the shadow again etc. because of the light bulb swaying. The audience feels calm at this point as the light bulb swaying slowly and quietly gives the impression that the drama is over. When Marion is driving away from Phoenix with the stolen money, the audience hear the voices in Marion head. We hear the voice of her boss, what he might say if he found out she had stolen the money. This is suspenseful because we are thinking what if her boss does know she stole the money†¦ what would he do? The voices make the audience feel anxious because they hear what Marion is thinking, and therefore they are put in Marion's position. We sympathise with Marion because we know what she is thinking. Although she stole the money, we don't feel sorry for Cassidy (the man whose money it was) he is a very arrogant man, he boasted about how much money he has and he tries to flirt with Marion. He doesn't respect Marion; he thinks he can easily get her because of his money. He says ‘I never carry as much as I can afford to lose. ‘ This tells us that he can afford to lose the money and it would be good to use the money for a good cause. If Marion had stolen the money from a charity, we would not sympathise with her because she is taking the money from a worthy cause. When Marion and Norman are in the parlour, Marion talks about Norman's mother. She suggests he puts her into a mental home. Norman's reaction to this suggestion builds suspense. He gets very angry and looks like he could get aggressive. He often compares people to birds as stuffing birds is his hobby. When Marion suggests his mother could go to a mental home, Norman compares his mother to one of his stuffed birds on the wall, he says how she is as harmless as one of them. He says how a mother is a boys best friend which makes us believe that he is very close to his mother but he is closer to her then anyone expected. Hitchcock has the title ‘The Master of Suspense'. I personally don't think that he deserves that title for this film. In 1960 he may have deserved it for this film as it was the first film like this, but now, in the year 2003, there are many films like this. It has suspense but I don't think it has enough suspense for him to have that title. Psycho is a horror/thriller film and it achieves the title of being a horror/thriller film better than it achieves the title of a suspenseful film.

Personal Finance Essay

Personal finance refers to the principal that is applied to the monetary decisions of an individual or a family unit. It addresses issues such as the ways in which the individuals or families obtain finance, budget, save and spend the monetary resources of a company over a given period of time while at the same time taking in account the financial risks and the future life events that are related to the businesses activities. The profits or loss of a company are derived by determining the incomes of a company and the expenses that are incurred by a company. If the incomes are more than the expenses the company generates profit for the company. If the expenses of the company are more than the incomes then the company incurs losses in the financial period of a company. Assumptions The income of Donna Terrell is estimated to be $3333 per month since it is assumed that he earns a salary that is equally distributed throughout the year. The expenses of Donna Terrell are also assumed to be evenly distributed throughout the year except in the months where Donna Terrell specified that the expenses were incurred in those months. After Sherman acquisition of his new job on June 2003 and his decision to assist Donna Terrell was a positive move since after the month of June the Donna’s business started to earn profits since in the previous months the business was incurring losses, but after June 2003 the company started to generate profits for the company, thus was in a position to run it affairs effectively (http://64. 233. 169. 104/search? q=cache:DmCJZy7zP6kJ) It is also assumed that Sherman would earn a salary that would be $1500 per the month that followed the month of June up to December 2003. In the first quarter of the year Donna business had been incurring losses from January to May 2008 since the amount of losses have been increasing rapidly since the expenses of the business were more than the incomes of the business. After Mr. Sherman decision to assist Mr. Donna in giving him financial assistance the business started to improve in its performance. The business incomes was greater than the expenses as from July to December of the Year 2003 and this contributed to the increased profits of the business as it continued with its operation until December 2003. As at December 2003 the Company had profits that were over $13000. The management of companies can run their activities if they ask for financial assistances from friends and also financial institutions since after the Mr. Sherman decision to assist Mr. Donna the performance of the company started to improve. The instances where the management of companies runs other business activities that generate revenue to a company this can contribute to the profitability of the company since the additional income increases the companies working capital that enables the company to generate as much revenue to the company hence its increased returns and finally this leads to the growth of the company. The management of companies should also plan their finances properly so as to avoid budget deficits as this can affect the performance of the company and also its reputation as this can result to reduce sales volume for a company hence in some cases due to the poor management of the companies finances the company go into liquidation that can lead to the closure of the company.

Henrik Ibsens Enemy of the People essays

Henrik Ibsen's Enemy of the People essays In Henrik Ibsen's play, Enemy of the People, Peter Stockmann is the real enemy of the people because he is primarily motivated by greed. He is a man with power and who does no mind using his influence to get what he wants despite who he has to hurt to get it. This paper will examine how Peter Stockmann's words and actions prove him to be the real enemy of the Our first indication that Peter might be less concerned with his fellow citizens than he is for himself comes from his reaction to his brother's news that the Bath establishment is a "permanent supply of poison" (I.143). Peter is very calm and seems to be only disturbed by the fact that such news could keep people from visiting the Baths. He asks Thomas, "Have you taken the trouble to consider what your proposed alterations would cost'" (II.155). Peter tells him that it would take nearly two years to complete the work and asks, "what are we to do with the Baths in the meantime' Close them' Indeed we should be obliged to. And do you suppose any one would come near the place after it had got about that the water was dangerous'" (II.156). These statements illustrate that Peter is more concerned with business than with the health of the community. Peter is also very arrogant. He does not think the people of the community deserve to know anything is they don't have to know it. He tells Thomas that "not a single word" (II.157) of the condition of the water should reach the public and that everything should be repaired in time in secret. When Thomas asks him if it is not the "duty of a citizen to let the public share in any new ideas" (II. 158), he tells him, "the public doesn't require any new ideas. The public is best served by the good, old established ideas it already has" (II.158). These statements indicate that Peter does not have much faith in the intelligence of the community. It also seems to reinforce hi...

Problem Solving and Data Analysis KeySAT MathConcepts

Problem Solving and Data Analysis KeySAT MathConcepts SAT / ACT Prep Online Guides and Tips SAT Math is divided intro three domains: Heart of Algebra Problem Solving and Data Analysis Passport to Advanced Math It's a good idea to get really familiar with what's going to be on the test, where it was derived, and what the SAT is really testing. This post will focus on one domain- Problem Solving and Data Analysis. This is an opportunity to get cozy with these concepts, and with the overall tapes of information that test-makers are looking for. Problem Solving and Data Analysis problems are all about applying your math knowledge to practical situations and looking at actual statistics instead of abstract, theoretical scenarios. Basic Information There are 17 questions in this domain (out of 58 total math questions). They aren't labeled or otherwise indicated on the test- you're never told which type of question you're working on. There are no Problem Solving and Data Analysis problems on the no-calculator section. You will always be permitted to use your approved calculator for questions from this domain- though you may not always need it. You will receive a subscore on a scale of 1-15 on this domain. There will be both multiple choice and grid-in questions. You'll be dealing with both single-step and multistep problems; sometimes, it's just a matter of reading the data and parroting it back, while other problems require a bit more manipulation of the numbers. General Concepts The test-makers want to know that you understand math thoroughly enough to use your skills in real-world settings. Quantitative reasoning is also crucial; you should be able to work with numbers and draw conclusions about what they imply. You’ll be working with a lot of numbers. Real-World Applications You should be able to build a representation of a problem. If a scenario is described to you, you should be able to model it mathematically by describing it with expressions and equations. You should know to consider the units involved. If there happens to be a shift of units (from feet to miles, or something like that), you should account for that as you calculate. You should keep track of the practical meaning of quantities. You're going to be representing real values with variables: don't forget what those variables represent. Also, be sure you understand how a change in one of these variables or quantities affects what's happening in the equation. For example, in a line ($y=mx+b$) with a positive slope (or value of $m$), increasing $x$ will also result in an increase in $y$. Data and Statistics There are a lot of graphs, charts, and tables that could be covered on the test. You should be capable of analyzing one-variable data in bar graphs, histograms, line graphs, and box-and-whisker plots- as well as two-variable data in scatterplots and two-way tables. In other words, you should be fluent in reading these various representations of data. You should be able to describe overall patterns. You'll have to identify positive and negative trends. You should be able to distinguish between linear and exponential growth. Specific Skills There are a number of skills that you'll want to be handy with on the day of the exam. In this section you'll find a discussion of these skills, including what they are and what they look like in action. In fact, let’s hope these skills aren’t all that new! Statistical Analysis The measures of center are arithmetic mean (average) and median. If they can't be calculated from what's given, you may still need to draw some conclusions about them. Even if you can't find the actual number, there may be a question about what possible values are, or how the values compare to another set of data. Outliers typically affect the mean, but not the median. The measure of spread to know is standard deviation. You've got to have the basic theory, but you won't need to calculate the exact value. You should be able to look at two sets of data and see which set is more spread out- that is, which has the greater standard deviation. Insofar as the precision of estimates is concerned, everything depends on the variability of the data and the sample size; smaller variability combined with a larger sample size makes for estimates that are more precise in terms of the actual population. Another tidbit of interest you should know is that randomization combats bias. You should, in context, be able to work with margins of error, which are affected by sample size and standard deviation. Confidence intervals should also be taken into account. The SAT always works with confidence intervals of 95%. This doesn’t mean that 95% of the population is necessarily described by the figure that’s been derived, just that we can be 95% certain that the descriptive figure that’s been reached is accurate. When analyzing the relationship between two variables, remember, correlation is not causation. If subjects for a sample are selected randomly, we can generalize to the entire population reasonably well. If subjects are randomly assigned to test groups, we can reasonably speculate about cause and effect. Otherwise, though, we’re out of luck. You should also be able to evaluate reports to make inferences, justify conclusions, and determine the appropriateness of data collection methods. Take a look at this problem: The correct answer here is (C). We know that removing one very high number from the set is not going to affect the median- the middle three values are all 12, so we know the median will still be 12, even if the middle of the data is shifted over one. The mean will shift somewhat if we don’t include the 24-inch measurement, but there are 20 other data points that anchor the mean at a relatively consistent value if any one value is removed. The range, however, will change from $24-8=16$ to $16-8=8$. The range gets cut in half if we remove the 24-inch measurement! That’s the measure that will change the most. Mathematical Models The domain of the SAT that we’re examining gives special attention to mathematical models. You must, therefore, be able to create and use a model. When two variables are presented in a graph, table, or other chart, you should be handy with analyzing and drawing conclusions with regards to the relationship between these variables. Relationships between variables can be modeled by functions, but remember the function is only a model! It may give scientifically accurate predictions, or it may just describe a general trend. You may be asked whether a model is good, acceptable, or entirely inappropriate. Let’s look at this problem: The geologist in the question provides a model regarding the country’s beach erosion. According to that model, beaches erode at a rate of 1.5 feet per year. 21 feet of erosion would therefore take 14 years, as $14(1.5)=21$. The functions you’re asked to work with may be linear, quadratic, and/or exponential. Linear and exponential are discussed in more detail below. Linear An important example of linear growth is simple interest, where you earn interest on your principal, each period, but not on any interest that has been added since that first deposit. This is modeled by the function: $A = P(1+rt)$. $P$ is the principal, $r$ is the interest rate, and $t$ is the amount of time interest has been accruing. Exponential An important example of exponential growth is compound interest, where you earn interest on the interest you’ve previously earned. This is modeled by the function: $A = P (1+r/n)^{nt}$, where $P$ is the principal, $r$ is the interest rate (typically annual), $n$ is the number of times the interest compounds per period (typically a year), and $t$ is the amount of time that has passed since the principal began accruing interest. Be careful! The stated rate of change may not be the same as the rate of change over time. This is typical of compound interest: You might take a loan at 9%, but if it compounds monthly, you’re really taking a loan at $(1+.09/12)^12 – 1 = 9.38%$ at the end of the year. On the other hand, you might make a deposit that accrues interest at a rate of 5%, but it compounds quarterly, so you’re really getting $(1+.05/4)^4 – 1 = 5.095%$ at the end of the year. Math and money are very closely linked. Ratios, Proportions, Units, and Percentages You’ll need to be familiar with direct proportionality/variation: $y = kx$, where $k$ is a unitless constant of proportion. This relationship may also be expressed as $x_1/y_1 = x_2/y_2$. You’ll need to know how percent increase and percent decrease work. Be careful about how you approach these problems; they can get a little tricky. Remember, for instance, that if you have a 20%-off coupon for an item that’s on a 20%-off sale, you won’t save 40%. You’ll save 36%, as you’ll pay 80% of 80% of the original price: $x(.8)(.8) = (.64)x = x - (.36)x$. Take a look at this pair of problems: This is the sort of situation where you’re asked to deal with quantities in very practical terms. These aren’t just numbers floating in and out of an abstract function; no, these numbers represent that annual budget, in thousands of dollars, for each of six different state programs in Kansas from 2007 to 2010. The first problem is asking for the approximate average rate of change in the annual budget for agriculture/natural resources in Kansas from 2008 to 2010. From 2008 to 2009, the budget grew by 127,099 thousands of dollars, or $127,099,000. From 2009 to 2010, the budget grew by 2,299 thousands of dollars, or $2,299,000. Thus, we add those two figures together, divide by two, and find that the average growth was $64,699,000, or, when rounding, (B). For the next problem, we are comparing the 2007-budget-to-2010-budget ratios across the various programs. We will first need to find those ratios: Agriculture/natural resources - $373,904/488,106=.766$ Education- $2,164,607/3,008,036=.7196$ Highways and transportation- $1,468,482/1,773,893=.8278$ Public safety- $263,463/464,233=.5675$ Out of these, the closest to human resources ($4,051,050/5,921,379=.6841$), is (B). Probability Two events are independent if one happening has nothing to do with another, like the sun shining and you eating a sandwich for lunch. The sun may shine, and you may eat a sandwich for lunch, but one does not cause or prevent the other. Two events are mutually exclusive if they cannot both occur, like me wearing a hat and me not wearing a hat. I can’t do both. For independent, non-mutually exclusive events: P(A and B) = P(A)*P(B), whereas P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events: P(A or B) = P(A) + P(B). There are other formulas for more complicated scenarios, but these will get you pretty far - they’re all you should need on the SAT. Let’s take a look at this problem: Twenty-five people passed the bar exam; of these, seven did not take the review course. So, the probability that the interviewed person in question did not take the bar exam is 7/25, or (B). Math and gambling are closely linked, too. It’s all about that probability. Conclusion This domain of the test is calculation-heavy, although there are some theoretical questions. These questions compose almost a third of the test. They cover, roughly: Statistical analysis Proportions Probability Modeling Real-world data Your answers will be scored to yield one of three subscores for the Math section. What’s Next? That was a fair amount of information. Digest it a little; then, a great next stop would be perusing our overall guide to SAT Math, including directions to a number of other great posts. Now, because Problem Solving and Data Analysis problems are so information-heavy, you may wish to practice with some word problems, to get used to that much verbal data being thrown your way. As you’re trying these practice problems, you’ll want to know how to use them to your best advantage. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial: