Information Theory and Thermodynamics

Information Theory and Thermodynamics In order to develop better tools, machines and technology we have had to develop our understanding of the physical world. This has allowed us to construct machines that are more capable than those preceding it. The French scientist Carnot was studying machines and was trying to understand how to make them better and more efficient. As part of his studies he calculated the maximum efficiency of any machine and was able to relate this to temperature. Carnots idea was to simplify the machine to its simplest form (this generality that makes it universal) and analyse that Carnot knew that machines of the time (and of today) work as a result of a temperature difference across the machine. In his time it was obvious, fire produced steam which turned a turbine that did work; today is not too different, all of our machines still need a temperature difference to make them work, however the temperature difference driving the machines may be at some distance, for example a power station producing electricity. Even wind, and solar require temperature differences to work. Analysing these machines further lead to concepts that we, perhaps, take for granted: work, power and energy notable examples. Whilst working on these concepts Boltzmann came up ideas that grew into statistical thermodynamics. It was extended and correctly describes a whole range of phenomena. The idea of thermodynamics is to relate various physical properties of a substance to the bulk behaviour of the constituent parts within. Microstates and Macrostates: Boltzmann realised that by knowing the number of different states that a system could be in and the number of configurations that each state would enable him to work out the probability of a particular state occurring. And that on average when something is observed it is more likely to be found in one of its more probable states. Many systems have lots of moving components and this means that over time a system will have evolved into a more probable state. This may now seem obvious, but it hadnt been pointed out explicitly at the time. A Macrostate is the global state of a system. For example if we consider a box with red, blue and green balls a possible macrostate might be to find all of the red balls are in the bottom left corner, whilst all of the others are randomly distributed in the rest of the box. Another example of a macrostate might be that the total electrical charge of block could be Coulombs. A Microstate is one particular configuration of the system that produces a macrostate. In the balls example if the balls are identical apart from colour we can permute the balls with the same colour amongst themselves and end up with different microstates. An example with the charged block might be that we have 4 particles each with charge as one microstate, and another might be to have 1 particle with and another with Below is a figure that represents a hypothetical macrostate of three colours of balls three particular microstates that can be used to achieve it. In the leftmost diagram we have a macrostate with all of the red balls in the bottom left corner, the other diagrams show different permutations of the balls that also achieve the desired macrostate. In order to calculate the probability of this state we would need to know how many combinations of it there are. This is a simple counting argument: we have 1 way of putting the green ball in its spot, two ways of putting the blue balls in their position and ways of arranging (we can pick any of the 5 to go in the corner, then any of the remaining 4 to go next to that, then any of the remaining 3 etc). There are a total of 8 balls and so the In general if there are objects we have possible arrangements; if we also have different types and if of them are of type 1 (say red), are of type 2 and are of type then we can find the total number of permuted arrangements with: We can use these two facts to calculate the number of accessible microstates of type , this is called the weight of the microstate and is denoted by, : The weight of a microstate is proportional to the probability of the system being in it. So one way to calculate the probability of being in the state is via: where the summation is over the weights of all the other possible microstates. A handy way to view a microstate is with a pack of cards (Birks bath), in a pack of playing cards the statistical weight of a club is 13 since there are 13 of then the statistical weight of a queen is 4. The probability of selecting a club card is the chances of picking out a club are times greater than picking out a queen. The statistical weight of the queen of hearts is 1. There is one obvious constraint that can always be imposed and that is that the total number of particles is the sum of the number of particles in each state: We can impose other constraints on the system as they are required later. Because the particles of each type are identical it is natural to assign a probability that a randomly selected particle is of type, , as: We are also able to define an Expectation value for the system. If we were interested in the average occupancy of each of the types we would have: which would represent the average occupancy of each type. If we were interested in the charge (or energy (I shall use for either) we would similarly have: Let us take some examples and compute the statistical weights, average occupancy and average energy (represented by the value of the type index e.g. if , the energy would be two units). I shall consider that the atoms are all identical apart from the energy that they have and that a macrostate is the same for each. For the first case let us assume that we have 5 atoms and the macrostate corresponds to an energy of 5 units. The table below shows that (for example) the microstate 3 has a weight of 20, this means that there are 20 microstates with the occupancy levels given that correspond to the macrostate We can tabulate the various combinations as below: microstate number Occupancy of type i weight probability n0 n1 n2 n3 n4 n5 1 4 0 0 0 0 1 5 0.0397 2 3 1 0 0 1 0 20 0.1587 3 3 0 1 1 0 0 20 0.1587 4 2 2 0 1 0 0 30 0.2381 5 2 1 2 0 0 0 30 0.2381 6 1 3 1 0 0 0 20 0.1587 7 0 5 0 0 0 0 1 0.0079 totals 15 12 4 2 1 1 126 1 Average occupancy 2.222 1.389 0.794 0.397 0.159 0.040 Table 3.1: Table showing occupancy levels for a 5 atom system with a macrostate of 5. This table was generated by finding all of the numbers that sum (in this case) to 5 which is the macrostate. It shows the number of atoms with a particular energy in the columns headed , the statistical weight of each microstate is in the weight column, the probability column next to it shows the probability of randomly selecting this microstate from a given macrostate (in this case 5 atoms and a total energy of 5). The row titled average occupancy shows the expected occupancy of an energy level of type , calculated from the table. Looking at the table there are two equally most likely microstate arrangements. The first of these corresponds to and , both occurring with a probability of 0.238. Another possible macrostate is listed below, this time we have 7 atoms and an energy of 7 units. The headings of the table are the same as in the previous example. We can see that the weight of the most probable microstate is 420 and that we have a probability of 0.245 of randomly selecting one of them. The occupancy levels are: microstate occupancy of type i weight probability n0 n1 n2 n3 n4 n5 n6 n7 1 6 0 0 0 0 0 0 1 7 0.004 2 5 1 0 0 0 0 1 0 42 0.024 3 5 0 1 0 0 1 0 0 42 0.024 4 5 0 0 1 1 0 0 0 42 0.024 5 4 2 0 0 0 1 0 0 105 0.061 6 4 1 1 0 1 0 0 0 210 0.122 7 4 1 0 2 0 0 0 0 105 0.061 8 4 0 2 1 0 0 0 0 105 0.061 9 3 3 0 0 1 0 0 0 140 0.082 10 3 2 1 1 0 0 0 0 420 0.245 11 3 1 3 0 0 0 0 0 140 0.082 12 2 4 0 1 0 0 0 0 105 0.061 13 2 3 2 0 0 0 0 0 210 0.122 14 1 5 1 0 0 0 0 0 42 0.024 15 0 7 0 0 0 0 0 0 1 0.001 totals 51 30 11 6 3 2 1 1 1716 1 Average occupancy 3.231 1.885 1.028 0.514 0.228 0.086 0.024 0.004 Table A3 2: a seven atom system with a total energy of seven A final example consists of a system of 10 atoms and a total energy of 9. As will be readily seen as the number of atoms and the energy increases the number of microstates corresponding to a given macrostate increases so does the size of the table. It was quite difficult to work out the number of combinations of energy that could occur and I wouldnt want to do it again for larger tables. In the next part we shall use the method of Lagrange multipliers to massively simplify the calculations for the probabilities and expectations. For the case of 10 atoms and an energy of 9 units. We see that the most probable microstates have the following occupancy levels: The most probable microstate has a probability of 0.1555, but there is another microstate that is only slightly less probable (a probability of 0.1300) and this has occupancy levels of: The two least likely microstates are the following: Both have a probability of 0.0002 which is very small indeed. Table 3 is below: d occupancy of each type i weight probability n0 n1 n2 n3 n4 n5 n6 n7 n8 n9 1 9 0 0 0 0 0 0 0 0 1 10 0.000205677 2 8 1 0 0 0 0 0 0 1 0 90 0.00185109 3 8 0 1 0 0 0 0 1 0 0 90 0.00185109 4 8 0 0 1 0 0 1 0 0 0 90 0.00185109 5 8 0 0 0 1 1 0 0 0 0 90 0.00185109 6 7 2 0 0 0 0 0 1 0 0 360 0.00740436 7 7 1 1 0 0 0 1 0 0 0 720 0.014808721 8 7 1 0 1 0 1 0 0 0 0 720 0.014808721 9 7 1 0 0 2 0 0 0 0 0 360 0.00740436 10 7 0 2 0 0 1 0 0 0 0 360 0.00740436 11 7 0 1 1 1 0 0 0 0 0 720 0.014808721 12 7 0 0 3 0 0 0 0 0 0 120 0.00246812 13 6 3 0 0 0 0 1 0 0 0 840 0.017276841 14 6 2 1 0 0 1 0 0 0 0 2520 0.051830522 15 6 2 0 1 1 0 0 0 0 0 2520 0.051830522 16 6 1 2 0 1 0 0 0 0 0 2520 0.051830522 17 6 1 1 2 0 0 0 0 0 0 2520 0.051830522 18 6 0 3 1 0 0 0 0 0 0 840 0.017276841 19 5 4 0 0 0 1 0 0 0 0 1260 0.025915261 20 5 3 1 0 1 0 0 0 0 0 5040 0.103661045 21 5 3 0 2 0 0 0 0 0 0 2520 0.051830522 22 5 2 2 1 0 0 0 0 0 0 7560 0.155491567 23 5 1 4 0 0 0 0 0 0 0 1260 0.025915261 24 4 5 0 0 1 0 0 0 0 0 1260 0.025915261 25 4 4 1 1 0 0 0 0 0 0 6300 0.129576306 26 4 3 3 0 0 0 0 0 0 0 4200 0.086384204 27 3 6 0 1 0 0 0 0 0 0 840 0.017276841 28 3 5 2 0 0 0 0 0 0 0 2520 0.051830522 29 2 7 1 0 0 0 0 0 0 0 360 0.00740436 30

Analysis of an Article on Obesity in America Essay -- Article Review

Obesity kills at least 111,000 Americans per year (Greenstreet 107). The government has made many approaches to reshape our food system and attempt to force us to buy the foods that make us fat. Especially during our recession, it is that much easier to buy fast foods because it simply is the cheaper thing to do. We have many needs as human beings that need to be met, with food being one of the most important and being in this recession has made us easy targets for the government. Organic foods and less-fatty foods are more expensive these days so even health-savvy people try to find cheaper alternatives and look for the positives in these not-so-healthy foods. Due to this, many people believe that the government and its power to control how expensive or cheap food is sold for is the biggest reason for obesity in America but in retrospect, it is simply our own fault because we make the decision to save money and eat less nutritiously over spending more money on the best food for yo ur diet. The reason for the growing population of obesity is not due to the government creating this epidemic because they in turn are trying to help out the growing obese population. Also, the obese population is constantly growing because of the personal choices of the people, the environment around them and the genetics of each individual. Immediately in the subtitle of the article, Greenstreet is quick to declare â€Å"how corporations and the US Government create the obesity epidemic† (Greenstreet 107). He makes the government seem like they are the main enemies and contributors to the growing obesity epidemic, â€Å"the government takes an extremely damaging and passive-aggressive role in contributing to a national health crisis...† (Greenstreet 107). ... ...): 1095-1105. Raj, Manu and R. Krishna Kumar, â€Å"Obesity in children & adolescents.† Indian Journal of Medical Research 132.5 (2010): 598-607. Kouzoukas, Demetrios L. â€Å"Legal Preparedness for Obesity Prevention and Control: The Structural Framework and the Role of Government.† Journal of Law 37 (2009): 24-27 "Major Crops Grown in the United States | Ag 101 | Agriculture | US EPA." US Environmental Protection Agency. N.p., n.d. Web. 1 May 2011. . "Obesity and Genetics." Columbia St. Mary's Medical Moment. N.p., Web. 1 May 2011. . "Ten ways to distinguish between healthy and unhealthy food." Choosing and cooking healthy food. N.p., n.d. Web. 1 May 2011. .

True Love: Hermia and Lysander

True Love Love is a strong-filled emotion, a bond which is shared between two persons. Love adds to the enchantment and beauty of life. Love has the power to lift the spirits of the persons who share this pure sentiment and is also capable of eliminating the controversies, jealousies and barriers existent due to blood lineage which may try to harm lovers. Egeus, Hermia’s Father, goes to Duke Theseus for assistance with his predicament. Theseus gives Hermia the option to either marry Demetrius, the man his father has deemed worthy of her, or for her to live a barren life as a nun.As Hermia heard what was to come, she replies to Theseus as she defends her love, †So I will grow, so live, so die, my lord, Ere I will yield my virgin patent up unto his lordship whose unwished yoke my soul consents not to give sovereignity. † Hermia’s pale cheeks and melancholic look reflected the sorrow settling in her spirit as she lost her right to love with her heart but in the eyes of another. The situation in which Hermia and Lysander are due to Egues complaint reveals the dominant male perspective of a fatherin society.Lysander in the situation they are in comforts Hermia by saying, â€Å"The course of true love never did run smooth. † Lysander assured her that they are only going through a phase which all lovers undergo but they will be able to conquer. In response to the Dukes options offered to Hermia, she and Lysander plan to elope in the woods and go to Lysander’s aunt. Lysander suggests to his love,†Therefore hear me, Hermia: I have a widow aunt a dowager of great revenue; and she hath no child. From Athens is her house remote seven leagues; and she respects me as her only son.There gentle Hermia, may I marry thee†¦Ã¢â‚¬  Hermia replies to him, â€Å"In that same place thou hast appointed me tomorrow truly will I meet with thee. † Hermia‘s and Lysander’s love is always put to the test by Egeus’ rejection of Lysander. In the forest, their love is put to the test simply by the fact that Demetrius is always after Hermia and tries to prevent her from eloping with Lysander. Their love is also trialed by Puck who confuses the Athenian lad which Oberon had sent him to put the love potion on.Puck was to place the potion on Demetrius for him to respond to Helena’s love but instead Puck placed it on Lysander’s. Throughout the plot of the story, Hermia always had the option to give up on Lysander’s love and stay with the lad her father had chosen for her, but she always had in mind to follow her heart and not give up on her love due to small adversities. Lysander is worthy of Hermia’s love and proves to be a brave lad who was willing to take risks in order to be with Hermia.While being with the Duke, Lysander tries to convince them that he is financially stable to be with Hermia by saying, â€Å"I am my lord, as well possessed. My love is more than his; my fortune every way as fairly ranked- if not with vantage- as Demetrius. † Through all adversities, He never left Hermia unprotected nor did he give up. Lysander comforts Hermia with his company and words of advice. Lysander was with Hermia in times of need as in the Dukes resolution.Lysander conquered all obstacles that came in between the love that he had for Hermia and proved he was truly worthy of Hermia’s love with his actions. The theme of forbidden love is reflected by the characters of Hermia and Lysander who live life as a daily battle in struggle to maintain their love alive. Even though â€Å"supernatural† powers and mountain-high problems may come in the way of true love, in the end love will always be victorious. Hermia and Lysander are an example of a couple who faced challenges on the way but the prize-being together as a couple, was far more rewarding in the end.

Importance of interview

Importance of interview To many firms, the interviewing process has always been a challenge to most of the human resource personnel in charge of this section in the employee recruitment process. As a result most of the organizations try to take the initiative of improving employees by taking their human resource personnel through the appraisal process.Advertising We will write a custom essay sample on Importance of interview specifically for you for only $16.05 $11/page Learn More This process is aimed at improving the employee’s ability and efficiency in carrying out an interview that enables the organization to recruit the desired individual with the desired skills. In this appraisal session, the trainer uses speeches to communicate with his/her audience, giving out brochures and video clips were necessary to explain his points (Laakmann, 2011). It is first of all necessary for the interviewer to be prepared before the actual interview is started in order to ensure that th e best candidate is selected with minimum errors. To start with the interviewer should be on the right track, he/she must be able to identify the goals of the interview and understand them clearly. This may be formulated through the identification of the present state of the firm, its needs in terms of the manpower, the quality and integrity of the preferred personnel. The interviewer should further be able to estimate the expected expenditure in the process, and expressly specify the estimated cost to be incurred on the employed personnel by the firm. This should be estimated based on what the firm can be able to afford at the time as salary to the additional employees, and the anticipated productivity of the individual to the output of the organization (Laakmann, 2011). After the preparation of this information, it should be passed to other colleagues in order to improve the performance and coordination of the team of interviewers.Advertising Looking for essay on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More As the team of interviewers, we should be able to review the material presented by the applicants taking note that a resume will always give more information about the applicant than an application letter. The next step includes the systematic classification of all the application letters and resumes initially received from the prospective interviewees, following the posting of the job in an advertisement (Glasser, 2007). The material should be screened for consistency of information between the application letter and the resume. At this stage of the process, the personnel should be able to avoid generalization errors like the qualifying of unnecessary courses done by the some of the candidates. To create some level of order in the whole process, the documents of the candidates are then classified in to three groups. Group A (qualified), Group B (meet minimum requirements) and Grou p C (does not meet qualifications). The collection of documents that are categorized as qualified are then re-reviewed to determine the best candidates that should be taken through an interview. While the rest are kept as contingency applications that may be used in case the person initially selected fails to turn out as expected. Several other methods may be used by the interviewer in the selection process of the preferred candidate, for example, a telephone interview (Cosentino, 2011). This may be done with utmost discretion by avoiding asking irrelevant questions that may not be related to the job, to minimize on the risk that may arise for example, the discrimination acts that may be due to asking questions about the interviewee’s race.Advertising We will write a custom essay sample on Importance of interview specifically for you for only $16.05 $11/page Learn More The next process is the actual interviewing process between the representative of the company or the employer himself with the candidate. To begin with, the human resource department of the firm may call the applicants directly themselves, or schedule the interviews through the use of recruitment specialists. However, there are some general guidelines that may be used by the firm to ensure good results are achieved (Cosentino, 2011). In the scheduling of the interviewing process, the interviewees should be allotted equal time for the process without any form of discrimination. This ensures that the process is fair and just to the interviewees. Adequate time should be allowed between two consecutive interviews, this will help the interviewers to get enough time to arrange the details of the completed interviewee. Simultaneously, sufficient time should be allocated for candidates going and coming to the office to do so freely. The candidates should be informed before they come for the interview about the venue, the specific time and the day of the interview. This will enable the interviewee to plan their activities and allocate adequate time for the interview. The applicants should be well informed about the company before they come for the interview, this will be a sign of interest in the company and its activities. In return they will understand company activities and what to expect from the employment. The candidates may further be instructed to bring job related documentations such as, the work models or recommendation letters where applicable. Several methods may be used by the firm to get more information from the candidate that can help in the selection process like the use of questionnaires, or direct questions asked by the interviewer. At this point fliers of some of the questions are distributed to the audience. In most of the companies, the interviewing process is done through question and answer sessions between the interviewer and the candidate; however, these questions must be well devised for them to retrieve the desired info rmation from the candidate on his/her abilities (Cosentino, 2011). Using direct questions like those that require a yes or no answer should be limited as they restrict information obtained from the candidate. The interviewer should use open ended questions like; tell me about your worst experience? These types of questions are the best to be used as they challenge the candidate to tell what he/she thinks is important and necessary in the prevailing circumstances. The answers are then used by the interviewer to judge the credibility and potential of the interviewee.Advertising Looking for essay on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More He/she may also make use of the situational questions that help to imply the type of reactions to expect from the applicant. These give the candidate the challenging context of the job like situation. The answers offered by the candidate are then used to assess their ability to identify the imperative circumstances in the job, analyze them, and provide reasonable solutions (Darling, 2009). Besides, some of the questions may be applied with the intention of getting general information about the candidates; these are recommended for use for a start up organization or first interviews before the final one is done (Posegate, 2008). Several of the questions may include; Questions used to identify previous work experience, for example. What are some of your key functions and responsibilities in your current job? Identify a time in your employment that you worked and achieved all you could? Questions used to establish the expectations of the interviewee on the Job being applied. What are the reasons that made you to apply for this position? Why do you think you should be hired for this position? Questions used to identify the candidate’s attitude towards management. What do you think are the most significant roles of a manager? Describe the type of directions that you prefer from a supervisor? Identification of the employee’s interpersonal skills, with reference to what the firm needs. How do you convince others to do what you want? Have you ever had conflict with the boss? How did you approach her/him and what solutions did you get? Were you satisfied with the solution? We need for you to describe a situation where you have a project in mind and you lack the necessary cash, how will you persuade your employer to grant you the cash. In some of the jobs, the firm may need someone who is creative and the only way to identify if for sure that person is creative is the use of questions whose answers require a creative mind. For instance, asking the cand idate to explain what he has done to improve the level of efficiency, effectiveness and ways to make work easier in his/her initial occupation (Glasser, 2007). Furthermore, in the assessment of whether the interviewer has a vision or not and his ability to understand the needs of the company, the interviewer may use questions like; have you ever been offered the position of leading a project? Explain how you were able to create and introduce direction in the team? Some positions in the firm may need an individual with good leadership abilities and the necessary influence on other people through inspiration of others, charisma and spurring. This kind of person may be identified through the use of well formulated questions, that lead to well thought out answers, for example, describe your approach to decision making and problem solving that make you unique? Or if you were to recommend for the transfer of certain functions from one department to another, what are some of the main facto rs that you will consider? These questions give the interviewee the chance to display his ability to make quick and creative solutions to the normal challenges that arise in the day to day work environment (Darling, 2009). After all the interviews have been done and the desired individuals have been identified. The personnel are supposed to develop a list of job related questions that should be used to verify the referees of all the candidates. Departments should carry out their own checks where necessary and if external help is required, one should conduct the staff recruitment specialists. We verify the interviewee’s referees for the following three reasons; To confirm employment; To substantiate new skills learned during the interview. To obtain employment recommendation. On the completion of the above procedures, a formal job offer is presented to the candidates. This is done later in form of an engagement letter and contract of employment based on the terms of the spec ific industry in which the firm operates (Posegate, 2008). References Cosentino, M. (2011). Complete Case Interview Organization. New York: Pre-press Publishers. Darling, T. (2009). How to Get Into Consulting Firms: A Surefire Case Interview Method. Boston: Person publishers. Glasser, C. (2007). Complete Case Interviewing Preparation. Chicago: Linder schrelber-Genster. Laakmann, G. M. (2011). Cracking the Coding Interview: 150 Programming Questions and Solutions. San Francisco: Brooks Cole publishers. Posegate, A. (2008). Climbing The Corporate Ladder. London: Front Row Press.

What Are Good SAT Scores for Colleges 101 Schools + Advice

What Are Good SAT Scores for Colleges 101 Schools + Advice SAT / ACT Prep Online Guides and Tips As you apply to college, it's important to understand how high of an SAT score you will need to aim for on test day. This raises the question:what aregood SAT scores for colleges? And notjust any colleges, but your colleges specifically? In this article, we’ll examine the SAT scores needed for college and how these scores can varydue todifferences in factors such as school prestige and competitiveness. We’ll then show you how to look for average SAT scores for colleges and how to set your own SAT goal score. What Are Good SAT Scores for Colleges? First off, what are good SAT scores for colleges? In reality, there's no single answer to this question because good SAT scores for universities vary depending on where you’re applying. For some schools, an SAT score of 1400 will be significantly high, whereas for others (i.e., top-20 colleges) it’ll be fairly low. As you might've guessed, ultra-competitive,top-ranked schools typically look for some of the highest SAT scores in applicants. Below is a chart containing thetop 25 US schools (as ranked by US News) and their ranges of SAT scoresfor incoming students. This data highlights the SAT score you'll need to get in order to give yourself the best shot at securing admissioninto ahighly competitive school.For each school, we give you theaverage SAT score, 25th percentile score, and 75th percentile score of incoming students. A 25th percentile score means that 25% of students scored at or below this threshold, while a 75th percentile score means that 75% of students scored at or below this threshold. Thus, the 25th and 75th percentiles represent the middle 50% SAT scores of admitted applicants- the average SAT score range for a particular school.GoodSAT scores for universities are usually those in the 75th percentile or higher (i.e., anything above the middle 50%). Note:For those curious about what kinds of SAT scores are required for Ivy League schools, I’ve bolded all eight Iviesin the table below. This should make it easier to compare the SAT scores of Ivies with those of non-Ivies. SAT Scores for Top 25 US Schools School US News Ranking 25th %ile SAT Score 75th %ile SAT Score Avg SAT Score Princeton 1 1430 1570 1500 Harvard 2 1460 1590 1520 Columbia 3 (tie) 1450 1580 1515 MIT 3 (tie) 1490 1570 1528 UChicago 3 (tie) 1480 1580 1530 Yale 3 (tie) 1420 1590 1505 Stanford 7 1390 1540 1465 Duke 8 (tie) 1390 1580 1485 Penn 8 (tie) 1420 1560 1490 Johns Hopkins 10 (tie) 1460 1580 1520 Northwestern 10 (tie) 1420 1560 1490 Caltech 12 (tie) 1530 1590 1560 Dartmouth 12 (tie) 1430 1560 1478 Brown 14 (tie) 1405 1570 1488 Vanderbilt 14 (tie) 1400 1550 1475 Cornell 16 (tie) 1390 1550 1470 Rice 16 (tie) 1490 1580 1535 Notre Dame 18 1370 1520 1445 UCLA 19 (tie) 1240 1490 1365 WUSTL 19 (tie) 1470 1570 1505 Emory 21 1350 1520 1435 Georgetown 22 (tie) 1350 1520 1435 UC Berkeley 22 (tie) 1330 1530 1430 USC 22 (tie) 1300 1500 1400 Carnegie Mellon 25 (tie) 1430 1560 1495 UVA 25 (tie) 1290 1470 1365 As you can see from this chart, the SAT scores you’ll need for top 25 schools vary slightly but are overall quite high.Of these schools, UCLA has the lowest SAT scores: the middle 50% of its incoming students scored between 1240 and 1490, or the 80th and 98th percentiles. By contrast,Caltech maintains the highest SAT scores:only 25% of incoming studentsscored at or below 1530- an extremely impressive SAT score in the 99th percentile! Even more impressive, a whopping 75% of Caltech students scored at or below a near-perfect score of 1590. Top schools are like center brownies: lots of people compete for them, but only a few will win access to one. But what if you’re not interested in applying to only top-25 schools? To lend you a hand, we've gathered SAT score information for 76 additional schools.All of the schools selected for this listare relatively well known- some more so in their respective regions- andvary from large public institutions to small liberal arts colleges. Whereas some are extremely competitive, others are more laid-back. But all are definitely worth considering for college! All schools below areorganized alphabetically.To find a specific school, use ctrl + F to type in the name of the school you're searching for. Note that University of California schools are listed using "UC." SAT Scores for 76 Popular Schools School 25th %ile SAT Score 75th %ile SAT Score Avg SAT Score American University 1180 1350 1260 Amherst College 1430 1560 1492 Baylor University 1190 1360 1275 Binghamton University 1290 1431 1361 Boston College 1320 1490 1405 Boston University 1300 1480 1380 Bowdoin College 1290 1510 1390 Brigham Young University (BYU) 1210 1410 1310 California Polytechnic State University (Cal Poly) 1220 1400 1293 Chapman University 1190 1360 1270 Claremont McKenna College 1420 1560 1490 College of William and Mary 1300 1480 1390 Drexel University 1160 1360 1260 George Washington University(GWU) 1280 1440 1355 Georgia Institute of Technology (Georgia Tech) 1090 1520 1295 Harvey Mudd College 1470 1570 1520 Indiana University Bloomington 1140 1350 1246 Lehigh University 1270 1430 1347 Loyola Marymount University 1180 1360 1269 Miami University 1190 1380 1285 Michigan State University(MSU) 1100 1320 1204 Middlebury College 1320 1510 1404 New York University (NYU) 1290 1490 1382 Northeastern University 1370 1520 1445 Ohio State University(OSU) 1260 1450 1344 Pace University 1070 1240 1137 Pennsylvania State University (Penn State) 1160 1340 1247 Pepperdine University 1200 1390 1294 Pitzer College 1310 1490 1394 Pomona College 1370 1530 1450 Rensselaer Polytechnic Institute(RPI) 1320 1500 1399 Rutgers University 1190 1400 1300 Scripps College 1290 1460 1384 Stony Brook University- SUNY 1210 1410 1304 Syracuse University 1160 1350 1255 Temple University 1130 1310 1221 Texas AM University 1140 1360 1252 Texas Christian University (TCU) 1130 1330 1230 Trinity College 1190 1440 1320 Tufts University 1410 1540 1475 Tulane University 1330 1490 1410 UC Davis 1120 1360 1240 UC Irvine 1170 1410 1286 UC Riverside 1090 1300 1179 UC San Diego(UCSD) 1140 1380 1257 UC Santa Barbara(UCSB) 1270 1500 1385 UC Santa Cruz 1160 1370 1263 United States Military Academy(West Point) 1185 1400 1300 United States Naval Academy 1250 1450 1410 University of Alabama 1050 1280 1177 University of Arizona 1100 1340 1182 University of Cincinnati 1120 1340 1233 University of Colorado Boulder(CU Boulder) 1150 1345 1248 University of Connecticut (UConn) 1110 1390 1250 University of Florida 1240 1410 1318 University of Georgia (UGA) 1200 1370 1281 University of Illinois at Urbana-Champaign(UIUC) 1340 1500 1420 University of Iowa 1100 1400 1240 University of Massachusetts Amherst (UMass) 1180 1360 1269 University of Miami 1220 1410 1316 University of Michigan 1330 1500 1415 University of Minnesota, Twin Cities 1270 1480 1358 University of North Carolina at Chapel Hill (UNC) 1260 1440 1347 University of Pittsburgh 1240 1418 1330 University of Rochester 1250 1490 1370 University of Texas at Austin (UT Austin) 1160 1390 1275 University of Texas at Dallas (UT Dallas) 1220 1430 1315 University of Vermont 1180 1350 1259 University of Washington 1190 1420 1310 University of Wisconsin- Madison 1280 1450 1359 Vassar College 1370 1510 1420 Villanova University 1250 1440 1345 Virginia Polytechnic Institute and State University (Virginia Tech) 1180 1360 1268 Wake Forest University 1260 1440 1350 Wellesley College 1360 1530 1437 Williams College 1400 1570 1468 School 25th %ile SAT Score 75th %ile SAT Score Avg SAT Score The list above is only a fraction of the length of Santa's naughty-or-nice list. Want to learn more about the SAT but tired of reading blog articles? Then you'll love our free, SAT prep livestreams. Designed and led by PrepScholar SAT experts, these live video events are a great resource for students and parents looking to learn more about the SAT and SAT prep. Click on the button below to register for one of our livestreams today! How to Find Average SAT Scores for Colleges With these two charts, we've given you- in addition to the 25th and 75th percentile SAT scores for each school- the average SAT scores of admitted applicants. These averages tell us what kinds of SAT scores you shouldaim for in order to match (or even possiblyexceed!) the qualifications of previously admitted students. But where can you findaverage SAT scores for colleges? The two best resources to look for SAT averages are ourPrepScholar database andofficial school websites. Method 1: Use the PrepScholar Database We at PrepScholar maintain a robust databaseyou can use to get more information onthe SAT scores needed for college. Start by typing in "[School Name] PrepScholar"or "[School Name] PrepScholar SAT"on Google. For example, here's the page I got when I searched for "university of oregon prepscholar": Click the link to either your school'sAdmission Requirements page orSAT Scores and GPA page in our database. I decided to look at the University of Oregon's Admission Requirements page(the first link in the screenshot above). Once on your school's PrepScholar page, scroll down to look for a section about its SAT scores. Straight away, you should be able to spot your school'saverage SAT score in a blue banner: If you'd like to see the 25th and 75th percentile SAT scores for your school as well, simply scroll down to look at the percentile chart: This is all you need to do to find the average SAT scores for colleges. However, if you’re having trouble locating a specific school in our PrepScholar database, move on to Method 2. Method 2: Use Official School Websites This method involves lookingfor SAT score information on aschool's official website.The easiest way to do this is to hop on Google, search for "[School Name] average SAT scores," and then click any links to official pages discussing SAT scores for your school. Another (slightly less convenient) method is tobrowseyour school'swebsite and intermittently usectrl + F to look for anymentions of SAT scores. The best pages to searchare those offering information onadmission statistics, the new freshman class, and facts and figures. That said, not allschools report average SAT scores. Whereas some won't release any SAT score information at all,other schools might report SAT scores of admitted applicants in the form of 25th and 75th percentile scores. One example of this is Princeton, whichoffers middle 50% SAT score ranges for both sections on the SAT. According to this Ivy League school, the middle 50% is 730-790 for Math and 700-770 for Evidence-Based Reading and Writing. In other words,25% of students scored1430 or below and 75% of students scored 1560 or below. Although this range isn’tthe same as an average, it does give us the information we ultimately want to know:what kind of SAT scores are considered better than average (and below average) at this particularschool. This freakishly beautiful kitten is anything but average. How to Set an SAT Goal Score We've seen how widely SAT scores for universities can vary; now, it’s time to figure out what score you'll need for your colleges specifically. In other words, what shouldyourSAT goal score be? A goal score is the SAT score most likely to get you into at least one of the colleges you're applying to (excluding safety schools). Ideally, it'll get you into all of them! Because SAT expectations can vary greatly by school and because there's such an enormous array of colleges you can apply to,your SAT goal score will be yours and yours alone.Other students might have higher or lower goal scores than you- but none of that matters. In the end, what does matter is your goal score’s likelihood of getting you into the college of your dreams! To find your SAT goal score, follow these three simple steps. Step 1: Make a Chart First off, make a table for the schools you're applying to and their 25th/75th percentile SAT scores. You may download our worksheet or draw a table similar to the one below. On the left, list all the schools you plan to apply to (excluding any safety schools you’re about90% certain you’ll get into). Here's an example: School 25th Percentile 75th Percentile UT Austin Texas AM Baylor TCU Step 2: Find SAT Score Info Online Your next step is to look for SAT score information for each of the schools in your table.To do this, follow the same steps as outlined in Method 1 for finding average SAT scores for colleges. Once again, here are the steps you'll need to take: Step 1: Search for "[School Name] PrepScholar SAT" on Google and click on the PrepScholar page for your school (either the Admission Requirements page or SAT Scores and GPA page will work). Step 2: Scroll down to the SAT section on this page to find a chart listing the 25th percentile, 75th percentile, and average SAT scores for this school. Step 3: Recordthe 25th and 75th percentile scores in your chart. In addition to using our database, you can search for "[School Name] SAT scores" on Google and look for official web pagesfor your school. Many schools will report either average SAT scores or the middle 50% of SAT scores(which is what you'll want for your chart). As a reminder, the minimum score in a 50% range is the 25th percentile, and the maximum is the 75th percentile. Once you've found SAT score information for all your schools, your chart should look like this: School Name 25th Percentile 75th Percentile UT Austin 1160 1390 Texas AM 1140 1360 Baylor 1190 1360 TCU 1130 1330 Step 3: Find Your Target Score Now, you’ll use the information in your chart to findyour target SAT score. To do this, simply look for the highest 75th percentile score in your chart.This will be your SAT target score. You must hit this (or near this) score in order to give yourself the best chance of admission to all the schools you're applying to. In this case, my goal score would be 1390 (for UT Austin), as this is the highest score in my chart. To figure out your (estimated) goal scores for each section (Evidence-Based Reading and Writing + Math), you candivide your goal score by 2.So a composite 1390 goal score would come out to a 690-700 EBRW goal score and a 690-700 Math goal score. My goal score? 100% completion in Breath of the Wild. (Brett Chalupa/Flickr) Summary: What Are Good SAT Scores for Colleges? Simply put, there is no one definition for good SAT scores for colleges. On the contrary, the SAT scores needed for college can vary significantly depending on schools' SAT expectations and where you’re applying. While some institutions might look for scores in the 99th percentile, others might accept scores closer to the national average. In general, good SAT scores for colleges are those that arein the 75th percentile or higher for your schools.Such a scoreshould elevate you well above the average SAT scores for yourschools, ultimately allowing you tostand apartfrom other applicants. Tofind average SAT scores for colleges, we recommend perusingeither our PrepScholar database or your schools' official websites. Finally, to set an SAT goal score, just follow these three easy steps: Step 1: Make a chart with all of the schools you're applying to(excluding safety schools) and their 25th and 75th percentiles. Step 2: Find SAT score information online by using either our database or your schools' official websites. Record the 25th and 75th percentilesin your chart. Step 3: Locate the highest75th percentile score in your chart.This will be your SAT goal score, as it's the one most likely to get you accepted to all the schools you're applying to. What’s Next? Still curious about good SAT scores for colleges?Read all about average SAT scores to see how they vary for different groups of test takers and learn what great, good, and poor SAT scores look like. Need additional help with setting an SAT goal score? Check out our step-by-step guide on how to seta target score for your schools. Readyto get the best SAT score you can get?With our completely customizable prep program, you can target your weaknesses and hone the skills you'll need most for test day. We also offer a ton ofexpert SAT tips and tricks to help you get the score you need for college! Disappointed with your scores? Want to improve your SAT score by 160 points?We've written a guide about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

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