M119L06-page7

# M119L06-page7 - point is still the population mean not x...

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(Lesson 6: Measures of Spread or Variation; 3-3) 3.21 Mean SD VAR Population (Size N ) μ σ 2 Sample (Size n ) x s s 2 The formula for sample variance is given by: s 2 = x x ( ) 2 n 1 The formula for sample SD is then given by: s = x x ( ) 2 n 1 Note 1: How does this differ from the formula for ? The population mean, , is presumably unknown, so we replace it with the sample mean, x . We also replace the population size, N , with n 1 . But …. Note 2: Why n 1 , not n ? Why is s the square root of a “tilted” average of the squared deviations from the sample mean, x ? The appropriate reference
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Unformatted text preview: point is still the population mean, , not x . The sample data values are more naturally clustered around their sample mean than around the population mean. In order to make s 2 a better estimate for 2 , the population variance, we inflate our estimate by dividing by n − 1 instead of n . Remember, for example: 1 4 > 1 5 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ . Then, s 2 will be an unbiased estimator of 2 in that it does not have an automatic tendency to consistently over- or underestimate 2 ....
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