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Question

Find out quartile deviation and coefficient of quartile deviation of the following series:
28, 18, 20, 24, 30, 15, 47, 27

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Solution

Arranging the data in ascending order.
Sr. No. 1 2 3 4 5 6 7 8
Observation 15 18 20 24 27 28 30 47


In order to find the quartile deviation in case of individual series, we need to find out the values of third quartile and first quartile using the following equations:

Q1 = Size of N+14th item

or, Q1= Size of 8+14th item

or, Q1= Size of 2.25th item

or, Q1= Size of 2nd item + 14Size of 3rd item-Size of 2nd item
or, Q1=18+1420-18

Q1 = 18.5

Q3 = Size of 3N+14th

or, Q3 = Size of 6.75th item
or, Q3 = Size of 6th item + 34Size of 7th item-Size of 6th item
or, Q3=28+3430-28or, Q3=27+342or, Q3=28+1.5 Q3=29.5Quartile deviation (Q.D.)=Q3-Q12or, Q.D.=29.5-18.52or, Q.D.=112 Q.D.=5.5Coefficient of Quartile deviation=Q3-Q1Q3+Q1 or, Coefficient of Q.D. =29.5-18.529.5+18.5 or, Coefficient of Q.D. =1148Coefficient of Q.D. =0.229=0.23

Hence the Q.D. of the series is 5.5 and Coefficient of the Q.D. is 0.23


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