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Published byCory Copeland Modified over 8 years ago
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Measuring Variability for Symmetrical Distributions
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Standard Deviation The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)
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The Formula The formula is easy: it is the square root of the Variance. What is the Variance?
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Variance The average of the squared differences from the Mean.
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Why square? To calculate the variance follow these steps: Work out the Mean (the simple average of the numbers)Mean Then for each number: subtract the Mean and square the result (the squared difference). Then work out the average of those squared differences.
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Example You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
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Find the mean first 600 + 470 + 170 + 430 + 300 = 1970 1970/ 5 (dogs) = Mean = 394
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Next Find the Distance between each dog height and the mean Dog HeightMeanDistance 600394206 47039476 43039436 300394-94 170394-224
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variance To calculate the Variance, take each difference, square it, and then average the result:
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Standard Deviation And the Standard Deviation is just the square root of Variance. Variance: 21,704 Standard Deviation: 147.32
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Useful? And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean
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Example 1 What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125? Find the Mean: 100 Variance: Standard Deviation
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Did you get it right? PopulationMeanDistanceSquared 12510025625 12110021441 100 00 96100-416 83100-17289 75100-25625 Variance: 332.667 Standard Deviation: 18.23
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What is the standard deviation? Ten friends scored the following marks in their end-of-year math exam: 23%, 37%, 45%, 49%, 56%, 63%, 63%, 70%, 72% and 82% Standard Deviation: 16.9%
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Standard Deviation A booklet has 12 pages with the following numbers of words: 271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314 Standard Deviation: 22.6
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