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Question -

The yield of wheat and rice per acre for 10 districts of a state is as under
Calculate for each crop,
(i) Range
(ii) QD
(iii) Mean’Deviation about Mean
(iv) Mean Deviation about Median
(v) Standard Deviation
(vi) Which crop has greater variation?
(vii) Compare the value of different measures for each crop.



Answer -

(i) Range
(a) Wheat Highest value of distribution (H) = 25
Lowest value of distribution (L) = 9
Range = H – L = 25 – 9 = 16
(b) Rice Highest value of distribution (H) = 34
Lowest value of distribution (L)=12
Range = H – L = 34 – 12 = 22
(ii) Quartile Deviation
(a) Wheat Arranging the production of wheat in increasing order 9, 10, 10, 12, 15, 16, 18, 19, 21, 25
= Size of 8th item + 0.25 (size of 9th item – size of 8th item)
= 19 + 0.25(21 – 19)
= 19 + 0.25 × 2
= 19 + 0.50 = 19.50
Quartile Deviation = 
(b) Rice Arranging the data of production of rice
12, 12, 12, 15, 18, 18, 22, 23, 29, 34 item
= 2.75 th item
= Size of 2nd item + 0.75 (size of 3rd item – size of 2nd item)
= 12 + 0.75(12 – 12) = 12 + 0.75 × 0
= 12
= 8.25th item
= Size of 8th item + 0.25 (size of 9th item – size of 8th item)
= 23 + 0.25(29 – 23)
= 23 + 0.25 × 6
= 23 + 1.5
= 24.5
Quartile Deviation = 
(iii) Mean Deviation about Mean
(a) Wheat
(b) Rice
(iv) Mean Deviation about Median
(a) Wheat
(b) Rice
(v) Standard Deviation
(a) Wheat
(b) Rice
(vi) Coefficient of Variation
(a) Wheat
Rice crop has greater variation as the coefficient of variation is higher for rice as compared to that of wheat.
(vii) Rice crop has higher Range, Quartile Deviation, Mean Deviation about Mean, Mean Deviation about Median, Standard Deviation and Coefficient of Variation.

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