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Unformatted text preview: 1 WEEK 8 Wed, Oct 20 DESCRIPTIVE STATISTICS and GRAPHICAL DISPLAYS (Background material is in Chapter 1) Overview of Data Types and Data Collection (Chap 1, Sec 1) Measurement processes applied to subjects or entities produce data. Usually many variables are measured for which data are recorded. You must understand the measurement process and the selection process (and the possible filtering of subjects out of the study after their selection) before you can truly evaluate the importance and usefulness of the data. Discuss and give examples of each of the following types of data. Categorical Data (sometimes coded numerically) Numerical Data Project 2010 US Census Short Form Discuss Data Collection Measurement Process Selection Process Subjects Data 2 Numerical Data Distributions Percentiles and Quartiles (Chap 1, Sec 2) Review of Percentiles for Probability Distributions. We learned how to get percentiles of normal distributions in Chapter 4. Recall that there we were working with random variables that take values on the line (numerical values) and the concept of a 100pth percentile, say, p = .95 for the 95 th percentile. This percentile is a position x that splits the distribution into two parts with P(X x) = .95 and P(X > x) = .05. Technically, this is a solution x to the equation F(x) = .95 where F is the cumulative distribution function of the continuous random variable. Example. N(90, 17). Let X have a normal distribution with mean 90 and standard deviation 17. The Texas Instruments programmers provide the solution for normal distributions. For example, the 95 th percentile is given by invNorm(.95,90,17) which returns the value 117.96. If you were to use the z-Table, you first find that the 95 th percentile of the standard normal distribution is between 1.64 or 1.65. Using 1.64 we determine the 95 th percentile of N(90, 17) with the equation x = 90 + (1.64)17 = 117.88. Finding the 100pth Percentile for a Numerical Data Distribution (n data points) using the textbooks method. (We assume 0 < p < 1.) Here is the algorithm that you can execute without using software....
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- Summer '10