For the same continuous distribution (Example 13), calculate the standard deviation by the step-deviation meth

Worked Examples · Example 15

Q. For the same continuous distribution (Example 13), calculate the standard deviation by the step-deviation method, taking deviations from 40 and dividing by the common factor 5.

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With $A = 40$ , $c = 5$ : $\sum fd' = 4$ , $\sum fd'^2 = 472$ , so $\sigma = \sqrt{11.79} \times 5 = 17.168$ .

Working table (with $d = m - 40$ and $d' = \dfrac{d}{5}$ ).

C.I.	f	m	d = m − 40	d′ = d ÷ 5	fd′	fd′²
10–20	5	15	−25	−5	−25	125
20–30	8	25	−15	−3	−24	72
30–50	16	40	0	0	0	0
50–70	8	60	+20	+4	+32	128
70–80	3	75	+35	+7	+21	147
Total	40				+4	472

Standard deviation (multiply back by the common factor $c = 5$ ). …

Q.For the same continuous distribution (Example 13), calculate the standard deviation by the step-deviation method, taking deviations from 40 and dividing by the common factor 5.