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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Find the mean deviation and its coefficient from the given data.
Class lnterval Frequency (f)
17.5-22.5 2
22.5-27.5 4
27.5-32.5 6
32.5-37.5 8
37.5-42.5 6
42.5-47.5 4
47.5-52.5 2
52.5-57.5 2
✓

Answer

Calculation of Mean Deviation and from its Coefficient Arithmetic Mean
Class Interval Mid value (m) Frequency (f) fm $|\text{D}|=|\text{m}-\bar{\text{X}}|\bar{\text{X}}=36.2$ $\text{f|D|}$
17.5-22.5 20 2 40 16.2 32.4
22.5-27.5 25 4 100 11.2 44.8
27.5-32.5 30 6 180 6.2 37.2
32.5-37.5 35 8 280 1.2 9.6
37.5-42.5 40 6 240 3.8 22.8
42.5-47.5 45 4 180 8.8 35.2
47.5-52.5 50 2 100 13.8 27.6
52.5-57.5 55 2 110 18.8 37.6
    $\sum\text{f}=34$ $\sum\text{fm}=1230$   $\sum\text{f|D|}=247.2$
$\bar{\text{X}}=\frac{\sum\text{fm}}{\sum\text{f}}$
$=\frac{1230}{34}=36.17-36.2$
Mean Deviation (MD) $=\frac{\sum\text{f|D|}}{\sum\text{f}}$$=\frac{247.2}{34}=7.27$
Coefficient of MD $=\frac{\text{MD}}{\text{Mean}}$$=\frac{7.27}{36.2}=0.20$

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