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Exercise 10.2 · Q6

Q.Calculate standard deviation for the following set of scores: 40, 38, 42, 60, 72, 54.

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

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

  1. Data: 40,38,42,60,72,5440, 38, 42, 60, 72, 54; n=6n=6.
  2. Sum: 40+38+42+60+72+54=30640+38+42+60+72+54=306, so xˉ=306/6=51\bar x = 306/6 = 51.
  3. Deviations xi−xˉx_i - \bar x: −11,−13,−9,9,21,3-11, -13, -9, 9, 21, 3.
  4. Squared deviations: 121,169,81,81,441,9121, 169, 81, 81, 441, 9. …

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