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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Calculate quartile deviation and coefficient of quartile deviation from the data given below:
320, 400, 450, 530, 550, 580, 600, 610, 700, 780, 800
✓

Answer

S. No. 1 2 3 4 5 6 7 8 9 10 11
X 320 400 450 530 550 580 600 610 700 780 800
$\text{Q}_1=\Big(\frac{\text{N}+1}{4}\Big)^{\text{th}}\text{item}$
$=\frac{11+1}{4}=\frac{12}{4}=3^\text{rd}\text{item}=450$
$\text{Q}_3=3\Big(\frac{\text{N}+1}{4}\Big)^{\text{th}}\text{item}$
$=\frac{3}{4}(11+1)=9^{\text{th}}\text{item}=700$
$\text{Q.D.}=\frac{\text{Q}_3-\text{Q}_1}{2}$
$=\frac{700-450}{2}=\frac{250}{2}=125$
Cofficient of Q.D. $=\frac{\text{Q}_3-\text{Q}_1}{\text{Q}_3+\text{Q}_1}$
$=\frac{700-450}{700+450}=\frac{250}{1,150}=0.217$

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