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Supplement_2

# Supplement_2 - SUMMARY STATISTICS SUMMARY STATISTICS...

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≈≈≈ SUMMARY STATISTICS ≈≈≈ SUMMARY STATISTICS Documents prepared for use in course C22.0103.001 , New York University, Stern School of Business The standard deviation page 3 Computing a covariance and correlation from data page 5 Gary Simon, 2005 revis ed by Avi Giloni on September 1, 2005 Cover photo: Blydenburgh Park, Smithtown, Long Island 1

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≈≈≈ SUMMARY STATISTICS ≈≈≈ 2
FG FG FG FG THE STANDARD DEVIATION FG FG FG FG The empirical rules regarding standard deviations are these: About 2 3 of the values in a list are between x - s and x + s . About 95% of the values in a list are between x - 2 s and x + 2 s . These can give us a good feel for what kind of answers we should get in assessing standard deviation, but certainly serious calculation will need a serious method. Here are four methods for getting a standard deviation. We’ll talk first about the sample standard deviation, used when you think your data values represent some subset of a population. There is a distinction between sample standard deviation and population standard deviation. It’s not usually a big deal. Method 1: This is the definition. The formula for the sample standard deviation s is s = 1 1 2 n xx i bg We often define S xx = i i n = b 2 1 , so that s = g 1 xx S n . Example: Consider this list of 5 values: 28 32 31 29 39 Start by finding the total 159 and hence the average 159 = 31.8. Now note the deviations from average and their squares. 5 Value Deviation Deviation 2 28 -3.8 14.44 32 0.2 0.04 31 -0.8 0.64 29 -2.8 7.84 39 7.2 51.84 TOTAL 0.0 74.80 The value 74.80 is S xx .

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Supplement_2 - SUMMARY STATISTICS SUMMARY STATISTICS...

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