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Question
In the previous question, calculate the relative measures of variation and indicate the value which, in your opinion, is more reliable.
Solution
(i) Coefficient of Range
(a) Wheat
Coefficient of Range = `(H - L)/(H + L)`
= `(25 - 9)/(25 + 9)`
= `16/34 = 0.47`
(b) Rice
Coefficient of Range = `(H - L)/(H + L)`
= `(34 - 12)/(34 + 12)`
= `22/46 = 0.48`
(ii) Coefficient of Quartile Deviation
(a) Wheat
Coefficient of Quartile Deviation = `(Q_3 - Q_1)/(Q_3 + Q_1)`
= `(19.50 - 10)/(19.50 + 10)`
= 0.32
(b) Rice
`Q_1 = 12, Q_3 = 24.5`
Coefficient of Quartile Deviation = `(Q_3 - Q_1)/(Q_3 + Q_1)`
= `(24.5 - 12)/(24.5 + 12)`
= 0.34
(iii) Coefficient of Mean Deviation from Mean
(a) Wheat
Coefficient of `MD_{overlinex} = (MD_{overlinex})/overlineX`
= `4.3/15.5 = 0.28`
Coefficient of `MD_{M} = (MD_{M})/M`
= `4.3/15 = 0.29`
(b) Rice
Coefficient of `MD_{overlinex} = (MD_{overlinex})/overlineX`
= `6/19.5`
= 0.31
Coefficient of `MD_{M} = (MD_{M})/M`
= `5.7/18 = 0.32`
(iv) Coefficient of Variation
(a) Wheat
CV = `sigma/overlineX xx 100`
= `5.04/15.5 xx 100 = 32.51`
(b) Rice
CV = `sigma/overlineX xx 100`
= `7.16/19.5 xx 100 = 36.71`
The coefficient of variation is more reliable than all other measures.
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