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4667 15 example 2 calculate range and its co

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Unformatted text preview: widely used. Demerits: 1. It is very much affected by the extreme items. 2. It is based on only two extreme observations. 3. It cannot be calculated from open-end class intervals. 4. It is not suitable for mathematical treatment. 5. It is a very rarely used measure. 7.4 Quartile Deviation and Co efficient of Quartile Deviation : 7.4.1 Quartile Deviation ( Q.D) : Definition: Quartile Deviation is half of the difference between the first and third quartiles. Hence, it is called Semi Inter Quartile Range. Q − Q1 In Symbols, Q . D = 3 . Among the quartiles Q1, Q2 2 and Q3, the range Q3 − Q1 is called inter quartile range and Q 3 − Q1 , Semi inter quartile range. 2 144 7.4.2 Co-efficient of Quartile Deviation : Q 3 − Q1 Co-efficient of Q.D = Q 3 + Q1 Example 3: Find the Quartile Deviation for the following data: 391, 384, 591, 407, 672, 522, 777, 733, 1490, 2488 Solution: Arrange the given values in ascending order. 384, 391, 407, 522, 591, 672, 733, 777, 1490, 2488. n +1 10 + 1 Position of Q1 is = = 2.75th item 4 4 Q1 = 2nd value + 0.75 (3rd value – 2nd value ) = 391 + 0.75 (407 – 391) = 391 + 0.75 × 16 = 391 + 12 = 403 n +1 Position Q3 is 3 = 3 × 2.75 = 8.25th item 4 Q3 = 8th value + 0.25 (9th value – 8th value) = 777 + 0.25 (1490 – 777) = 777 + 0.25 (713) = 777 + 178.25 = 955.25 Q − Q1 Q.D = 3 2 955.25 − 403 = 2 552.25 = = 276.125 2 Example 4 : Weekly wages of labours are given below. Calculated Q.D and Coefficient of Q.D. Weekly Wage (Rs.) :100 200 400 500 600 No. of Weeks :5 8 21 12 6 145 Solution : Weekly Wage (Rs.) 100 200 400 500 600 Total No. of Weeks 5 8 21 12 6 N=52 Cum. No. of Weeks 5 13 34 46 52 N + 1 52 + 1 = = 13.25th item 4 4 Q1 = 13th value + 0.25 (14th Value – 13th value) = 13th value + 0.25 (400 – 200) = 200 + 0.25 (400 – 200) = 200 + 0.25 (200) = 200 + 50 = 250 N +1 th Position of Q3 is 3 = 3 × 13.25 = 39.75 item 4 Q3 = 39th value + 0.75 (40th value – 39th value) = 500 + 0.75 (500 – 500) = 500 + 0.75 ×0 = 500 Q 3 − Q...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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