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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
Find out quartile deviation and coefficient of quartile deviation of the following data:
Age (years): 0-20 20-40 40-60 60-80 80-100
No. of People: 4 10 15 20 11
✓

Answer

Age (Years) f c.f.
0-20 4 4
20-40 10 14
40-60 15 29
60-80 20 49
80-100 11 60
  $\Sigma\text{f}=60$  
$\text{Q}_1=\Big(\frac{\text{N}}{4}\Big)^{\text{th}}\text{item}$
$=\Big(\frac{60}{4}\Big)^{\text{th}}\text{item}$
$= 15^{th}$ item which lies in the class 40-60.
$\text{Q}_1=\text{l}_{1}+\frac{\frac{\text{N}}{4}-\text{c.f.}}{\text{f}}\times\text{i}$
$=40+\frac{15-14}{15}\times20$
$=40+\frac{1}{15}\times20$
$=40+1.33=41.33$
$\text{Q}_3=3\Big(\frac{\text{N}}{4}\Big)^{\text{th}}\text{item}$
$= 3 \times 15 = 45^{th}$​​​​​​​ item which lies in the class 60-80.
$\text{Q}_3=\text{l}_1+\frac{3\Big(\frac{\text{N}}{4}\Big)-\text{c.f.}}{\text{f}}\times\text{i}$
$=60+\frac{45-29}{20}\times20$
$=60+\frac{16}{20}\times20=76$
$\text{Q.D.}=\frac{\text{Q}_3-\text{Q}_1}{2}$
$=\frac{76-41.3}{2}=17.33$
Coefficient of $\text{Q.D.}=\frac{\text{Q}_3-\text{Q}_1}{\text{Q}_3+\text{Q}_1}$
$=\frac{76-41.33}{76+41.33}=\frac{34.67}{117.33}=0.29$

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