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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Calculate standard deviation from the following data using step deviation method:
Marks: 0-10 10-20 20-30 30-40 40-50
No. of Students: 4 3 6 4 2
✓

Answer

Marks No. of Students (f) M.V. (X) $dx$ $dx'$ $dx'^2$ $fdx'$ $fdx'^2$
0-10 4 5 -20 -2 4 -8 16
10-20 3 15 -10 -1 1 -3 3
20-30 6 25 0 0 0 0 0
30-40 4 35 10 1 1 4 4
40-50 2 45 20 2 4 4 8
  $\Sigma\text{f}=19$         $\Sigma\text{fdx}'=-3$ $\Sigma\text{fdx}'^2=31$
S.D. $=\sqrt{\frac{\Sigma\text{fdx}'^2}{\Sigma\text{f}}-\Big(\frac{\Sigma\text{fdx}'}{\Sigma\text{f}}\Big)^2}\times\text{i}$
$=\sqrt{\frac{31}{19}-\Big(\frac{-3}{19}\Big)^2\times10}$
$=\sqrt{1.63-.03}\times10=\sqrt{1.60}\times10$
$=1.26\times10=12.6$

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