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Question

Calculate Quartile Deviation and its Coefficient from the following data:
Size 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50
Frequency 6 10 18 30 15 12 10 6 4


Solution

Size Frequency Cumulative Frequency
5−10 6 6
10−15 10 16
15−20 18 34
20−25 30 64
25−30 15 79
30−35 12 91
35−40 10 101
40−45 6 107
45−50 4 111
  Σf=N = 111  


Q1 = Size of N4th item
     = Size of 1114th item
     = Size of 27.75th item


27.75 item lies in group 15−20 and falls within 34th c.f. of the series

Q1=l1+N4-c. f.f×iHere,l=Lower limit of the class intervalN= Sum total of the frequenciesc.f.=Cumulative frequency of the class preceding the first quartile classf= Frequency of the quartile classi= Class intervalThus,Q1=15 + 27.75-1618×5or, Q1=15+11.75×518or, Q1=15+58.7518or, Q1=15+3.26Q1=18.26


Like wise,
Q3 = Size of 3N4th item
      = Size of 31114th item
      = Size of 83.25th  item

83.25th  item lies in the group 30-35 within the 33rd c.f. of the series.


Thus,Q3=l1+3 N4-c. ff×ior, Q3 =30 + 83.25-7912×5or, Q3=30+4.25×512or, Q3=30+21.2512or, Q3=30+1.77Q3=31.77

Quartile Deviation=Q3 - Q12=31.77-18.262=6.75
Coefficient of Q.D.=Q3 - Q1Q3+Q1=31.77-18.2631.77+18.26=13.5150.03=0.27

Economics
Sandeep Garg (2019)
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