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1 Central Tendency

# 1 Central Tendency - Dr Harvey A Singer School of...

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© 2006 by Harvey A. Singer 1 OM 210 Statistical Analysis for  Management Data Summarization: Part 1: Measures of Central Tendency Dr. Harvey A. Singer School of Management George Mason University

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© 2006 by Harvey A. Singer 2 Learning Objectives Describe any given data distribution in terms of its few summary numerical measures. Central tendency. Also referred to as central location. Describes the similarity of the data values. Measured in terms of being close to some characteristic and representative value. “Close” in value or location. Variability. Also referred to as variation, dispersion, scatter, or spread. Describes how different are the data values. Measured in terms of how far off are the values from some characteristic and representative value. “How far off” uses a distance measure.
© 2006 by Harvey A. Singer 3 Learning Objectives Shape. Describes how the data is distributed within the distribution. Skew vs. symmetry. Grouped data. When the raw data is missing or unavailable and only have the frequency distribution, reconstruct summary measures. Uses and inferences. To recognize questions that are statistical in nature and answer them by associating the appropriate statistic. To fully describe the data in terms of its basic characteristics and behavior. Without tables and charts. To generalize from the sample to the population or the process as a whole.

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© 2006 by Harvey A. Singer 4 Purpose To obtain snapshot representations of all of the sampled data. In terms of the just a few characteristic and representative measures. “Characteristic” and “representative” in the sense that these few values can stand for and in place of all of the data. Have a complete understanding of the data by the skillful use of these measures, without having to draw any diagrams. “Few” means no more than a handful. And usually less. So as to make useful inferences and judgments about the sample and the population from which it was drawn. Valid and true inferences before drawing histograms.
© 2006 by Harvey A. Singer 5 Numerical Data Properties and Measures Coeff. of Variation Numerical Data Mean Median Mode Midrange (Quartiles) Midquartile Central Tendency Range Interquartile Range Variance Standard Deviation Variabilit y Skew Shape Grouped Data (Quartiles) Symmetric Weighted mean Clustering

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© 2006 by Harvey A. Singer 6 Project Durations Sample of n = 11 projects for their completion times in whole days. Data in raw form (as collected). 24, 26, 24, 20, 27, 27, 28, 31, 49, 33, 38 Data rank-ordered and listed in an ordered array. 20, 24, 24, 26, 27, 27, 28, 31, 33, 38, 49 x min x max
© 2006 by Harvey A. Singer 7 Project Durations Based on the given sample data, what are the characteristic and representative values of project duration?

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