calculate Q.D. and it's coefficient from the following data: X: 31-40, 41-50, 51-60, 61-70, 71-80 & f: 40, 60, 20, 40, 25. in measures of dispersion.
Answers
Given :
X: 31-40, 41-50, 51-60, 61-70, 71-80
f: 40, 60, 20, 40, 25.
To Find : Q.D (quartile deviation)
coefficient of quartile deviation
Solution:
X f cf
30.5 - 40.5 40 40
40.5 - 50.5 60 100
50.5 - 60.5 20 120
60.5 - 70.5 40 160
70.5 - 80.5 25 185
185/4 = 46.25 > 40 lies in 40.5 - 50.5
Q₁ = 40.5 + 10 * ( 185/4 - 40)/60
= 40.5 + 1.04
= 41.54
(3/4)185 = 138.75 > 120 lies in 60.5 - 70.5
Q₃ = 60.5 + 10 * (138.75 - 120)/40
=60.5 + 4.6875
= 65.1875
Quartile Deviation =(Q3 – Q1) / 2
= ( 65.1875 - 41.54)/2
= 11.82375
coefficient of quartile deviation = (Q₃ - Q₁)/(Q₃ + Q₁)
= ( 65.1875 - 41.54)/(65.1875 + 41.54)
= 0.22
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