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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Calculate mean deviation from mean from the following data using direct method and assumed mean method: 2, 4, 7, 8, 9
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Answer

Direct Method:
X $\bar{\text{X}}=6|\text{D}|=|\text{X}-\bar{\text{X}}|$
2 4
4 2
7 1
8 2
9 3
$\Sigma\text{X}=30$ $\Sigma|\text{D}|=12$
$\bar{\text{X}}=\frac{\Sigma\text{X}}{\text{N}}=\frac{30}{5}=6$
$\text{M.D.}_{\bar{\text{X}}}=\frac{\Sigma|\text{D}|}{\text{N}}=\frac{12}{5}=2.4$
Assumed Mean Method:
X $\text{|D|}=|\text{X}-\text{A}|$
2 5
4 3
7 0
8 1
9 2
$\Sigma\text{X}=30$ $\Sigma|\text{D}|=11$
$\bar{\text{X}}=\frac{\Sigma\text{X}}{\text{N}}=\frac{30}{5}=6$
$\text{M.D.}_{\bar{\text{X}}}=\frac{\Sigma|\text{d}|}{\text{N}}=\frac{11}{5}=2.2$

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