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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion6 Marks
Question
From the following data, calculate coefficient of quartile deviation.
Wages less than: 10 20 30 40 50 60 70
No. of Workers: 5 8 15 20 30 33 35
✓

Answer

Note: Since we are given cumulative frequencies*, we will first convert them into simple frequencies.
Class Interval f c.f.
0-10 5 5
10-20 3 8
20-30 7 15
30-40 5 20
40-50 10 30
50-60 3 33
60-70 2 35
  $\Sigma\text{f}=35$  
Lower quartile/Q $=\Big(\frac{\text{N}}{4}\Big)^{\text{th}}\text{item}=\Big(\frac{35}{4}\Big)^{\text{th}}\text{item}=8.75$ which lies in the class 20-30$\text{Q}_1=\text{l}_1+\frac{\big(\frac{\text{N}}{4}\big)-\text{c.f.}}{\text{f}}\times\text{i}$
$=20+\frac{8.75-8}{7}\times10=21.1$
Upper quartile or $\text{Q}_3=3\Big(\frac{\text{N}}{4}\Big)^{\text{th}}\text{item} = 3 \times 8.75^{th}$ item $= 26.25^{th}$ item, which lies in class 40-50.$\text{Q}_3=\text{l}_1+\frac{3\big(\frac{\text{N}}{4}\big)-\text{c.f.}}{\text{f}}\times\text{i}$
$=40+\frac{26.25-20}{16}\times10=46.25$
Coefficient of Q.D. $=\frac{\text{Q}_3-\text{Q}_1}{\text{Q}_3+\text{Q}_1}$$=\frac{46.25-21.1}{46.25+21.1}=\frac{25.1}{67.7}=0.3$

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