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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Find the standard deviation by assumed mean method.
X 10 20 30 40 50 60
Frequency 4 6 9 8 5 10
✓

Answer

Calculation of Standard Deviation
X Frequency (f) d(X - A), A = 30 fd $fd^2$
10 4 -20 -80 1600
20 6 -10 -60 600
30 9 0 -0 0
40 8 10 80 800
50 5 20 100 2000
60 10 30 300 9000
  $\Sigma\text{f}=42$   $\Sigma\text{fd}=340$ $\Sigma\text{fd}^2=14000$
$\sigma=\sqrt{\frac{\Sigma\text{fd}^2}{\Sigma\text{f}}-\Big(\frac{\Sigma\text{fd}}{\Sigma\text{f}}\Big)^2}$
$=\sqrt{\frac{14,000}{42}-\Big(\frac{340}{42}\Big)^2}$
$=\sqrt{333.3-(8.09)^2}$
$=\sqrt{333.3-65.45}=\sqrt{267.85}$
$\therefore\sigma=16.37$

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