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5 Summary - Dr Harvey A Singer School of Management George...

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© 2009 by Harvey A. Singer 1 OM 210 Statistical Analysis for  Management Data Summarization: Part 5. Summary of Key Concepts Dr. Harvey A. Singer School of Management George Mason University
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© 2009 by Harvey A. Singer 2 Basic Sample Statistics Mean (simple arithmetic average; measures the expected value). The median is the value of the middle position of the rank-ordered data. If n is odd , the median is the actual middle value of the ranked data. If n is even, the median is the calculated average of middle pair of values of the ranked sequence. The median serves as a useful point of reference for distinguishing high vs. low values. ( 29 n n i i x x x n x n x + + + = = = 2 1 1 1 1
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© 2009 by Harvey A. Singer 3 Basic Sample Statistics The mode is the value or values that occur often and repeatedly. Measures the “typical” value or values. Midrange (measures the middle between the two extreme values). Midquartile (measure of central tendency of the inner (or central) half of the data, contained between the quartiles Q 1 and Q 3 ). 2 max min x x x mr + = 2 3 1 Q Q x mq + =
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© 2009 by Harvey A. Singer 4 Basic Sample Statistics Range (measures the total span of all the data). Interquartile range ( IQR ) (measures the span of the inner or central half of the data about the median, contained between the quartiles Q 1 and Q 3 ). Note: Calculate the quartiles as the medians of the upper and lower halves. min max x x R - = 1 3 Q Q IQR - =
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© 2009 by Harvey A. Singer 5 Basic Sample Statistics Sample variance (approximately the average squared deviation). Sample standard deviation (approximately the average deviation) is the square root of the sample variance. 2 s s = ( 29 = - - = n i i x x n s 1 2 2 1 1
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© 2009 by Harvey A. Singer 6 Some Derived Sample Statistics Coefficient of Variation , CV (measures relative variability, that is, variability of the data with respect to the mean).
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