Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the step-deviation method, dividing the

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Q. Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the step-deviation method, dividing the values by the common factor 5.

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With $c = 5$ : $x' = 1,2,5,6,10$ , mean $= 4.8$ , $\sum d'^2 = 50.80$ , so $\sigma = \sqrt{10.16} \times 5 = 15.937$ .

Step 1 — Divide the values by the common factor $c = 5$ (so $x' = \dfrac{X}{c}$ ), and find the mean of $x'$ : $\bar{x}' = \dfrac{1 + 2 + 5 + 6 + 10}{5} = \dfrac{24}{5} = 4.8$ .

Step 2 — Deviations of $x'$ from $\bar{x}'$ and their squares.

X	x′ = X ÷ 5	d′ = x′ − 4.8	d′²
5	1	−3.8	14.44
10	2	−2.8	7.84
25	5	+0.2	0.04
30	6	+1.2	1.44

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Q.Calculate the standard deviation of the values 5, 10, 25, 30 and 50 by the step-deviation method, dividing the values by the common factor 5.

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