An Introduction to the Bell Curve

A normal distribution is more commonly known as a bell curve.   This type of curve shows up throughout statistics and the real world.   For example, after I give a test in any of my classes, one thing that I like to do is to make a graph of all the scores. I typically write down 10 point ranges such as 60-69, 70-79, and 80-89, then put a tally mark for each test score in that range. Almost every time I do this, a familiar shape emerges. A few  students do very well and a few do very poorly. A bunch of scores end up clumped around the mean score. Different tests may result in different means and standard deviations, but the shape of the graph is nearly always the same. This shape is commonly called the bell curve. Why call it a bell curve? The bell curve gets its name quite simply because its shape resembles that of a bell. These curves appear throughout the study of statistics, and their importance cannot be overemphasized. What Is a Bell Curve? To be technical, the kinds of bell curves that we care about the most in statistics are actually called normal probability distributions. For what follows we’ll just assume the bell curves we’re talking about are normal probability distributions. Despite the name â€Å"bell curve,† these curves are not defined by their shape. Instead, an intimidating looking formula is used as the formal definition for bell curves. But we really don’t need to worry too much about the formula. The only two numbers that we care about in it are the mean and standard deviation. The bell curve for a given set of data has the center located at the mean. This is where the highest point of the curve or â€Å"top of the bellâ€Å" is located. A data set‘s standard deviation determines how spread out our bell curve is. The larger the standard deviation, the more spread out the curve. Important Features of a Bell Curve There are several features of bell curves that are important and distinguishes them from other curves in statistics: A bell curve has one mode, which coincides with the mean and median. This is the center of the curve where it is at its highest.A bell curve is symmetric. If it were folded along a vertical line at the mean, both halves would match perfectly because they are mirror images of each other.A bell curve follows the 68-95-99.7 rule, which provides a convenient way to carry out estimated calculations:Approximately 68% of all of the data lies within one standard deviation of the mean.Approximately 95% of all the data is within two standard deviations of the mean.Approximately 99.7% of the data is within three standard deviations of the mean. An Example If we know that a bell curve models our data, we can use the above features of the bell curve to say quite a bit. Going back to the test example, suppose we have 100 students who took a statistics test with a mean score of 70 and standard deviation of 10. The standard deviation is 10. Subtract and add 10 to the mean. This gives us 60 and 80. By the 68-95-99.7 rule we would expect about 68% of 100, or 68 students to score between 60 and 80 on the test. Two times the standard deviation is 20. If we subtract and add 20 to the mean we have 50 and 90. We would expect about 95% of 100, or 95 students to score between 50 and 90 on the test. A similar calculation tells us that effectively everyone scored between 40 and 100 on the test. Uses of the Bell Curve There are many applications for bell curves. They are important in statistics because they model a wide variety of real-world data. As mentioned above, test results are one place where they pop up. Here are some others: Repeated measurements of a piece of equipmentMeasurements of characteristics in biologyApproximating chance events such as flipping a coin several timesHeights of students at a particular grade level in a school district When Not to Use the Bell Curve Even though there are countless applications of bell curves, it is not appropriate to use in all situations. Some statistical data sets, such as equipment failure or income distributions, have different shapes and are not symmetric. Other times there can be two or more modes, such as when several students do very well and several do very poorly on a test. These applications require the use of other curves that are defined differently than the bell curve. Knowledge about how the set of data in question was obtained can help to determine if a bell curve should be used to represent the data or not.

Getting the Best Topics for Rogerian Essay

Getting the Best Topics for Rogerian Essay Topics for Rogerian Essay - Is it a Scam? Essay writing demands that you've got the adequate and effective writing skills to come up with a distinctive and exceptional paper. You can also purchase essays from us and find a writer to start from scratch. The essay meets the necessities of the assignment sheet. Various essays are written to serve several purposes and every student ought in order to know a lot of them. The Topics for Rogerian Essay Game An individual Cannot Censor the Information on the net. Social media sites are not anything more than tools for narcissists. Many should watch the things that they post on the web. Just because you delete something it doesn't signify that it's permanently deleted from the web. Contrary to other kinds of essays, you're attempting to convince your reader of something. When writing a Rogerian paper, it's fundamental to bear in mind the important points and the Rogerian argument ideas. Don't forget that virtually any paper can be become a sarcastic or humorous piece offered by you. If you're still on the lookout for assistance with your Rogerian essay, there are many places it is possible to turn to. Learn how funny argumentative essay topics can receive the interest of your tutor. By this time, you have probably already written lots of distinct kinds of essays, and you might have even written a Rogerian essay before realizing it. An argumentative essay requires you to choose a topic and have a position on it. A superior argumentative essay is going to be based on established or new research in place of only on your ideas and feelings. When you compose this kind of essay, you provide background info in a brief and concise fashion, as the primary portion of your bit of writing is argumentation. No matter what type of essay you're writing, a strong plan will allow you to have a larger impact. In addition, it helps simplify the writing process because you can develop an outline for your paper and quickly produce the ideas you wish to have in your article. The Toulmin System, an important facet of a well-planned paper, ought to be studied carefully. The Topics for Rogerian Essay Pitfall In fact, Rogerian rhetoric can be regarded as a peculiar variant of the democratic debate. In a Rogerian argument, you have to examine an issue from several viewpoints, showing empathy for the assorted perspectives. It is not just convincing but in addition drives to persuasion. A statement form creates a speaker defend their point, even though the ultimate objective is to come across a consensus. The point is that, by finding common ground, you are more inclined to be in a position to come across a way to solve the argument or disagreement. Even though the aim isn't necessarily to change the person who you are speaking to's mind, the Rogerian way is still considered a type of argumentation as you are persuading your opponent to at least respect your viewpoint. Balanced Your primary purpose is to be utterly objective and present your ideas and ideas of your opponents equally. When you are requested to opt for a great topic for your argument, start with something you're familiarized with. Toulmin arguments also incorporate a rebuttal section recognizing an opposing perspective. A Rogerian argument will help to soothe such a scenario, and it is not just convincing but also persuasive. It comes in handy by helping to conciliate such a situation. The conclusive paragraph should end with a closing statement about the advantages of either side of the problem but not the author presenting his preferred way to solve the problem discussed. By way of example, in college, you might be requested to compose a paper from the opposing perspective. So, you should research that topic as a way to specify the topic's scope. Give background information on the matter and add as many details as you are able to in order to earn a complete picture of the discussed issue. It's very difficult to acknowledge that a very simple phone call can end a person's life. Why gaming is the sole thing you're expert at. A cell phone is believed to be a distractive element which disturbs a man who drives a vehicle. It becomes an additional item in the driver's hand, so that the driver has only one hand to control the vehicle.

Pneumonia and Older Adults Free Essays

What is pneumonia? Pneumonia is a lung infection that can make you very sick. You may cough, run a fever, and have a hard time breathing. For most people, pneumonia can be treated at home. We will write a custom essay sample on Pneumonia and Older Adults or any similar topic only for you Order Now It often clears up in two to three weeks, but older adults, babies, and people with other diseases can become very ill. They may need to be in the hospital. You can get pneumonia in your daily life, such as at school or work. This is called community-associated pneumonia. You can also get it when you are in a hospital or nursing home. This is called healthcare-associated pneumonia. It may be more severe because you already are ill. This topic focuses on pneumonia you get in your daily life. What causes pneumonia? Germs called bacteria or viruses usually cause pneumonia. Pneumonia usually starts when you breathe the germs into your lungs. You may be more likely to get the disease after having a cold or the flu. These illnesses make it hard for your lungs to fight infection, so it is easier to get pneumonia. Having a long-term, or chronic, disease like asthma, heart disease, cancer, or diabetes also makes you more likely to get pneumonia. What are the symptoms? Symptoms of pneumonia caused by bacteria usually come on quickly. They may include: †¢Cough. You will likely cough up mucus (sputum) from your lungs. Mucus may be rusty or green or tinged with blood. †¢Fever. †¢Fast breathing and feeling short of breath. †¢Shaking and â€Å"teeth-chattering† chills. You may have this only one time or many times. †¢Chest pain that often feels worse when you cough or breathe in. †¢Fast heartbeat. †¢Feeling very tired or feeling very weak. †¢Nausea and vomiting. †¢Diarrhea. When you have mild symptoms, your doctor may call this â€Å"walking pneumonia. â€Å" How to cite Pneumonia and Older Adults, Papers