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Exercise 10.2 · Q5

Q.Find the standard deviation of the data 3, 6, 2, 1, 7, 5.

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Compute the mean, then the mean of squared deviations from the mean (variance), then its square root.

For nn observations x1,…,xnx_1,\ldots,x_n:

xˉ=∑xin,σ=∑(xi−xˉ)2n\bar x=\frac{\sum x_i}{n}, \qquad \sigma=\sqrt{\frac{\sum (x_i-\bar x)^2}{n}}

where xˉ\bar x = mean, σ\sigma = standard deviation.

  1. Data: 3,6,2,1,7,53, 6, 2, 1, 7, 5; n=6n=6.
  2. Sum: 3+6+2+1+7+5=243+6+2+1+7+5=24, so xˉ=24/6=4\bar x = 24/6 = 4.
  3. Deviations xi−xˉx_i-\bar x: −1,2,−2,−3,3,1-1, 2, -2, -3, 3, 1.
  4. Squared deviations (xi−xˉ)2(x_i-\bar x)^2: 1,4,4,9,9,11, 4, 4, 9, 9, 1. …

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