bus-stat-book1

Let y denote test 2 marks x 55 y 45 u v 10 10 203 mid

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Unformatted text preview: he variable y and denote these deviations by v. 3. Multiply uv and the respective frequency of each cell and unite the figure obtained in the right hand bottom corner of each cell. 4. Add the corrected (all) as calculated in step 3 and obtain the total fuv. 5. Multiply the frequencies of the variable x by the deviations of x and obtain the total fu. 6. Take the squares of the step deviations of the variable x and multiply them by the respective frequencies and obtain the fu2 Similarly get fv and fv2 . Then substitute these values in the formula 1 and get the value of ‘ r’ . Example 4: The following are the marks obtained by 132 students in two tests. Test-1 30-40 40-50 50-60 60-70 70-80 Total Test-2 20-30 2 5 3 10 30-40 1 8 12 6 27 40-50 5 22 14 1 42 50-60 2 16 9 2 29 60-70 1 8 6 1 16 70-80 2 4 2 8 Total 3 21 63 39 6 132 Calculate the correlation coefficient. Let x denote Test 1 marks. Let y denote Test 2 marks. x − 55 y − 45 u= v= 10 10 203 mid x mid y 55 65 4 2 0 - 0 12 1 2 8 1 0 45 0 8 2 0 5 22 0 0 -1 2 55 -2 -2 65 1 -2 75 = = -2 -20 40 18 -1 -27 27 4 0 0 0 0 1 29 29 11 2 32 64 14 8 3 24 72 24 132 0 24 96 71 3 38 232 71 0 10 8 3 -2 -6 12 10 r= fuv 16 3 5 2 f u fu fu2 fuv fv2 - 25 35 fv 29 75 v 27 45 f 10 35 21 -1 -21 21 14 0 16 0 0 8 0 0 2 0 63 0 0 0 0 -1 6 -6 0 14 0 1 9 9 2 6 12 3 4 12 39 1 39 39 27 0 1 42 0 2 2 4 4 1 4 6 2 12 6 2 12 24 20 N Σfuv - (Σfu ) (Σfv ) [ N Σfu 2 − (Σfu ) 2 ].[ N Σfv 2 − (Σfv) 2 ] 132 × 71 − 24 × 38 [132 × 96 − (24) 2 ] [132 × 232 − (38) 2 ] 9372 − 912 (12672 − 576) (30624-1444) 8460 8460 = = = 0.4503 109.96 × 170.82 18786.78 204 Check Example 5: Calculate Karl Pearson’ s coefficient of correlation from the data given below: Age in years Marks 18 19 20 21 22 0- 5 3 1 5- 10 3 2 10-15 7 10 15-20 5 4 20-25 3 2 x − 12.5 5 y − 20 v= 1 u= y mid x 18 2.5 19 - - v fv fv2 Fuv 4 -2 -8 16 -10 5 -1 -5 5 -7 - 17 0 0 0 0 - - 9 1 9 9 -5 - 20 - 5 2 10 20 -16 16 1 16 16 -9 3 2 6 12 -8 40 0 9 47 -38 0 6 50 -38 21 -2 3 - 22 -4 1 -4 -2 2 -4 -6 7.5 - - -1 3 - -3 0 0 12.5 - - 10 7 0 0 17.5 -4 22.5 3 -12 f u fu fu2 fuv 3 -2 -6 12 -12 -1 5 -5 -2 2 -4 7 -1 -7 7 -9 f 0 4 0 11 0 0 0 0 205 Check N Σfuv - (Σfu ) (Σfv ) r= [ N Σfu 2 − (Σfu )...
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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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