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Standard Deviation and Variance

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by

Katie Rademacher

on 12 November 2012

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Transcript of Standard Deviation and Variance

Standard Deviation and Variance What is the Standard Deviation? The Standard Deviation shows how spread out the numbers in a data set are from the mean. It is represented with the sign σ. The Formula Wait, what? represents the number of data points represents "the sum of" represents the first data point (the data point - the mean) squared the number of data points - 1 Still confused? Example A data set has the points 8, 10, 6, 4, and 2. The mean is 6. Find the standard deviation. σ = (8-6) + (10-6) + (6-6) + (4-6) + (2-6) 2 2 2 2 2 5 - 1 σ = 4 + 16 + 0 + 4 + 16 4 σ = 10 σ = 3.16 What is the Variance? The variance is the standard deviation squared. It too shows the difference of data points from the mean. Variance can be shown as σ 2 The Formula This formula is very similar to the standard deviation. Note here that sigma is squared. Do NOT find the square root of the rest of the problem! The problem now changes. Example A data set has the points 8, 10, 6, 4, and 2. The mean is 6. Find the variance. (8-6) + (10-6) + (6-6) + (4-6) + (2-6) σ 2 = 5-1 2 2 2 2 2 σ 2 = 4 + 16 + 0 + 4 + 16 4 σ 2 = 10 So what's the difference? Both show the difference of points from the mean The standard deviation is the square root of the variance The standard deviation is usually more helpful in interpreting data Questions? 2 Also, know that the formulas used in this presentation were to find the standard deviation and variance of a sample population.
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