M119L06-page5 - spread. The deviations effectively cancel...

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(Lesson 6: Measures of Spread or Variation; 3-3) 3.19 Back to Example 1 Find the population VAR and SD of the given data set. Show all work on exams! Data x ( ) Step 2 Deviations: x μ ( ) values Step 3 Squared Deviations: x ( ) 2 values 80 7.8 60.84 76 11.8 139.24 100 12.2 148.84 83 4.8 23.04 100 12.2 148.84 Step 1 : = 87.8 points See Note 2 below. Sum = 520.8 Do Steps 4, 5 . Note 1: You should fill out the above table row by row. For example, take the “80”, subtract off the mean, and then square the result: 80 Subtract 87.8 ⎯⎯⎯ 7.8 Square ⎯⎯ 60.84 Note 2: Why not use the sum or average of the deviations as a measure of spread? It is always 0 for any data set, so it is meaningless as a measure of
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Unformatted text preview: spread. The deviations effectively cancel each other out. This reflects the fact that the new mean of our recentered data set is 0. For this and for other theoretical reasons, we square the deviations before taking an average. What if we were to take the absolute values of the deviations before taking an average? The result would be the mean absolute deviation (MAD), which is discussed on pp.102-103 of Triola . Note 3 on Rounding: We were fortunate that exact values were easily written in the table. See Notes 3.02 for a reminder of our rounding rules for Chapter 3 ....
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This note was uploaded on 12/29/2011 for the course MATH 119 taught by Professor Kim during the Fall '09 term at SUNY Stony Brook.

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