4545 discrete series 2 find quartile deviation and

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Unformatted text preview: ion and its co-efficient for the following data. Income : Frequency: 110 120 130 140 150 160 170 180 190 200 50 45 40 35 30 Income Frequency 110 50 45 95 130 40 35 30 25 225 170 20 245 180 15 260 190 10 270 200 5 5 200 160 10 170 150 15 135 140 20 50 120 25 CF 275 (N+1) / 4 th item = 69 = 120 3(N+1) / 4 th item = 207 =160 Size of (275+1) / 4 th item Size of (276 / 4) th item = size of 69th cumulative frequency = 120 = Size of 3(N+1) / 4 th item = Size of 3 X (275 +1) / 4 th item = Size of 3 X69 th item = Sikkim Manipal University Size of (N+1) / 4 th item = Q3 = = Q1 Size of 207th cumulative frequency Page No. 190 Research Methodology Unit 11 = = 40/2 = 20 = (Q3- Q1) / (Q3 + Q1) = (160- 120 / (160+ 120) = 20/280 = Co-efficient of Quartile Deviation (160 –120) /2 = Quartile Deviation 160 .0714 Continuous Series Find quartile deviation for the following series Marks : 0-20 Income 40-60 60-80 80-100 10 Frequency : 20-40 30 36 30 14 Frequency CF 0-20 10 10 20-40 30 40 (N) / 4 th class = 20- 40 40-60 36 76 60-80 30 106 3(N) / 4 th class = 60-80 80-100 14 120 = lies in (N) / 4 th class = lies in (120) / 4 th class = lies in (30) th cumulative frequency class = Q1 lies in 20- 40 Q1 can be obtained by applying the interpolation formula = = 20 + (30 – 10) / 30 X 20 = 20 + 20/ 30 X 20 = 20 + 400/30 = 20 + 13.33 = Sikkim Manipal University L1 + (N/4) – m / f X C 33.33 Page No. 191 Research Methodology Unit 11 = lies in 3(30)th cumulative frequency class = Q3 lies in 60-80 class Q3 can be obtained by applying the interpolation formula = = 60 + (90 – 76) / 30 X 20 = 60 + (14/ 30) X 20 = 60 + 280/30 = 60 + 9.33 = 69.33 = (Q3- Q1) /2 = (69.33 –33.33) 2 = 36/2 = Quartile Deviation L1 + 3 (N/4) – m / f X C 18 Co-efficient of Quartile Deviation = (Q3- Q1) / (Q3 + Q1) = (69.33 –33.33) / (69.33 + 33.33) = 36/ 102.66 = .3505 Mean Deviation Range and quartile deviation do not show any scatter ness from the average. However, mean deviation and standard deviation help us to achieve the dispersion. Mean deviation is the average of the deviations of th...
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