ioe265f11-Lec02 - Lec02 Descriptive Statistics Topics I II...

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Lec02: Descriptive Statistics IOE 265 F11 1 1 Descriptive Statistics 2 Topics I. Concept of Location and Dispersion II. Measures of Location III. Measures of Dispersion IV. Box Plots
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Lec02: Descriptive Statistics IOE 265 F11 2 3 I. Location and Dispersion Most common descriptive statistics are related to either measuring location or dispersion (variation). Location ~ central tendency Dispersion ~ spread of distribution Classic example to demonstrate these concepts: Outcomes of Throwing Darts On or Off Location Low or High Dispersion 4 Lecture Exercise: Identify On/Off Target & High/Low Dispersion for each x x x x x x x x x x x x B. __________ D. __________ A. _________ C. __________
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Lec02: Descriptive Statistics IOE 265 F11 3 5 Target / dispersion analysis and general problem solving First, address problems in order of importance. Highest Priority – address features that have strongest cause- effect relationship with end-customer satisfaction. Next, we typically try to reduce dispersion, then shift mean to target as necessary to meet end- customer needs. Stabilize process Center Process as necessary 6 II. Measures of Location Mean Median Trimmed Mean
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Lec02: Descriptive Statistics IOE 265 F11 4 7 Mean Mean (also known as the average) is a measure of the center of a distribution. Typical notation used to represent the mean of a sample of data is ; Greek letter is used to represent the mean of a population . Example: suppose five students take a test and their scores are 70, 68, 71, 69 and 98. Mean = (70+68+71+69+98)/5 = 75.2 N X X X Mean N ... 2 1 X 8 Median Median (also known as the 50 th percentile) is the middle observation in a data set. Rank the data set and select the middle value. If odd number of observations, the middle value is observation [N + 1] / 2. If even number of observations, the middle value is extrapolated as midway between observation numbers N / 2 and [N / 2] + 1. Prior data values: 68, 69, 70, 71, and 98. Median is 70. If another student with a score of 60 was included, the new median would result in 69.5 (69 + 70 / 2).
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Lec02: Descriptive Statistics IOE 265 F11 5 9 Mean Vs. Median Which is a better measure of location for the following set of test scores?
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ioe265f11-Lec02 - Lec02 Descriptive Statistics Topics I II...

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