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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion4 Marks
Question
Find the standard deviation using the actual mean method.
X 2 3 4 5 6 7
Frequency 2 3 9 21 11 5
✓

Answer

Calculation of Standard Deviation
X Frequency(f) fX $\text{d}(\text{X}-\bar{\text{X}}),\bar{\text{X}}=5$ $d^2$ $fd^2$
2 2 4 -3 9 18
3 3 9 -2 4 12
4 9 36 -1 1 9
5 21 105 0 0 0
6 11 66 1 1 11
7 5 35 2 4 20
  $\Sigma\text{f}=51$ $\Sigma\text{f X}=255$     $\Sigma\text{fd}^2=70$
$\bar{\text{X}}=\frac{\Sigma\text{fX}}{\Sigma\text{f}}=\frac{255}{51}=5$
$\sigma=\sqrt{\frac{\Sigma\text{fd}^2}{\Sigma\text{f}}}=\sqrt{\frac{70}{51}}=\sqrt{1.37}$
$\sigma=1.17$

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