DobbinChapter1 Sec1.3.NormalDistRevFeb22012

DobbinChapter1 Sec1.3.NormalDistRevFeb22012 - CHAPTER 1...

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CHAPTER 1, Section 1.3 Revised Feb 2, 2012 If the overall pattern of a large number of observations is quite regular, we chose to describe it by a smooth curve called a density curve . A Density curve has the following properties: 1. It is on or above the horizontal axis. 2. The total area under the curve is 1.0000 or 100.00%. 3. The area under the curve and between any two values on the horizontal axis represents the percent or fraction of all observations that fall in that range, (probability of occurrence). 4. Because density curves are continuous distributions, the chance of any exact value occurring is 0; only an interval has a percent or a probability of occurring. The median of a density curve is the equal areas or equal counts point. The mean of a density curve is the balance point. For a left skewed density curve, the mean is lower or less than the median. For a symmetric density curve, the mean = the median. For a right skewed density curve the mean is higher or greater than the median. A density curve is an idealized model for a distribution of data. It is often used to describe the entire population of interest, and in this context the mean of the population is designated as µ , and the standard deviation as σ . When we take actual observations (generally a sample) we distinguish the mean of the sample observations as and the standard deviation as s . Lecture 3, Section 1.3 Page 1
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Normal Distributions are a particularly important class of density curves. These density curves are symmetric, unimodal, and bell-shaped. They have the following properties: They are all symmetric Their mean is equal to their median The standard deviation controls the spread of a normal curve. We can actually locate by eye on a normal curve. It is the point on the horizontal scale which is directly under the inflection points of the curve. Changing the mean,,
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This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue.

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DobbinChapter1 Sec1.3.NormalDistRevFeb22012 - CHAPTER 1...

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