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MEAN,MEDIAN AND PARTITION VALUES

MEAN,MEDIAN AND PARTITION VALUES. MEAN. DEFINETION OF CENTRAL TENDENCY. IT IS DEFINED AS THE REPRESENTATIVE OF A GIVEN DATA. SOME Eg . OF CTs ARE MEAN MEDIAN MODE LOWER QUARTILE UPPER QUARTILE DECILE PERCENTILE. TO FIND THE MEAN OF A RAW OR UNGROUPED DATA.

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MEAN,MEDIAN AND PARTITION VALUES

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  1. MEAN,MEDIAN AND PARTITION VALUES

  2. MEAN

  3. DEFINETION OF CENTRAL TENDENCY • IT IS DEFINED AS THE REPRESENTATIVE OF A GIVEN DATA. • SOME Eg. OF CTs ARE MEAN MEDIAN MODE LOWER QUARTILE UPPER QUARTILE DECILE PERCENTILE

  4. TO FIND THE MEAN OF A RAW OR UNGROUPED DATA. FORMAT : x1, x2, x3…………xn MEAN x = ∑xi/n Eg. 1, 2, 3, 4, 5, 6 X= = 21 = 3.5 6 6

  5. TO FIND THE MEAN OF UNGROUPED FREQUENCY DISTRIBUTION FORMAT : xffx x1 f1f1x1 x2 f2 f2x2 x3 f3 f3x3 . . . . . . xnfnfnxn ∑fi ∑fixi MEAN x = ∑fixi/∑fi

  6. TO FIND THE MEAN OF GROUPED FREQUENCY DISTRUBUTION(WHERE CI IS NON-CONTINUOUS) FORMAT : C.Ifmid value(x)fx 0-4 2 2 4 5-9 3 7 21 10-14 5 12 60 15-19 2 17 34 ∑fi ∑fixi MEAN: x = ∑fixi/∑fi

  7. TO FIND THE MEAN OF GROUPED FREQUENCY DISTRUBUTION(WHERE CI IS CONTINUOUS) FORMAT : C.Ifmid value(x)fx -0.5-4.5 2 2 4 4.5-9.5 3 7 21 9.5-14.5 5 12 60 14.5-19.5 2 17 34 ∑fi ∑fixi MEAN: x = ∑fixi/∑fi

  8. TO FIND THE MEAN WHEN CF IS GIVEN FORMAT 1 MARKSNO. OF STUDENTS(c.f)f below 10 5 5-0 = 5 below 20 9 9-5 = 4 below 30 17 17-9 = 8 below 40 29 29-17 = 12 below 50 45 45-29 = 16 C.Ifxfx 0-10 5 5 25 10-20 4 15 60 20-30 8 25 200 30-40 12 35 420 40-50 16 45 720 ∑f ∑fx USE X= ∑fixi/∑fi

  9. TO FIND THE MEAN WHEN CF IS GIVEN FORMAT 2 marksno. of students(c.f)f above 50 36 5 above 60 31 10 above 70 21 3 above 80 18 11 above 90 7 7 above 100 0 0 C.Ifxfx 50-60 5 55 275 60-70 10 65 650 70-80 3 75 225 80-90 11 85 935 90-100 7 95 665 ∑f ∑fx MEANx =∑fx/∑f

  10. CHANGE IN A MEAN IF a IS ADDED, SUBTRACTED MULTIPLIED OR DIVIDED TO EACH OBSERVATION THEN THE MEAN CHANGES ACCORDINGLY ie, a IS ADDED, SUBTRACTED MULTIPLIED OR DIVIDED TO THE MEAN eg. X1, X2 ……………………….XnX1+a,X2+a…………..Xn+a X= x1+x2+……………………….xnX= X+a n Eg.1,2,3,4,5,6 1+1,2+1,3+1,4+1,5+1,6+1 X= 3.5 X= 3.5+1 =4.5

  11. MEAN BY SHORTCUT METHOD FORMAT c.ifmid value(x)di=xi-Afidi 0-10 7 5 -20 -140 10-20 10 15 -10 -100 20-30 15 A=25 0 0 30-40 8 35 10 80 40-50 10 45 20 200 ∑fi ∑fidi USE MEAN x = A+ ∑fidi/ ∑fi

  12. MEAN BY STEP DEVIATION METHOD FORMAT c.ifmid value(x)di=xi-A/hfidi 0-10 7 5 -2 -14 10-20 10 15 -1 -10 20-30 15 A=25 0 0 30-40 8 35 18 40-50 10 45 220 ∑fi ∑fidi USE MEAN x = A+ h(∑fidi/ ∑fi)

  13. COMBINED MEAN LET, n1 AND n2 BE THE NO OF OBJECTS IN TWO GROUPS, LET, X1 AND X2 BE THE MEAN OF THE TWO GROUPS THEN THE COMBINED MEAN OF BOTH THE GROUPS IS GIVEN BY, X = n1x1+n2x1/n1+n2

  14. MEDIAN AND OTHER PARTITION VALUES

  15. MEDIAN FOR UNGROUPED DATA FORMAT 1 X1, X2, X3……………………………Xn n= odd ARRANGE X1, X2, …………Xn IN ASCENDING OR DESCEDING ORDER FIND THE VALUE OF OBSERVATION. THIS IS THE MEDIAN. Eg. 1 3 1 3 2 5 6 4 5 n=9(odd). )= 5thOBSERVATION AFTER ARRENGING IN ASCENDING/DESCENDING ORDER 1 1 2 3 3 4 5 5 6 5TH OBSERVATION MEDIAN = 3

  16. MEDIAN FOR UNGROUPED DATA FORMAT 2 IF n=EVEN FIND THE VALUE OF th OBSERVATION AFTER ARRANGING IN ASCENDING/DESCENDING ORDER. THE MEAN OF th AND THE NEXT OBSERVATION GIVES YOU THE MEDIAN Eg. 1 2 1 3 4 5 n=6 1 1 2 3 4 5 = 3rd OBSERVATION MEDIAN = = 2.5

  17. LOWER AND UPPER QUARTILE OF UNGROUPED DATA IF n = odd LOWER QUARTILE (Q1)= th OBSERVATION UPPER QUARTILE (Q3)= OBSERVATION IF n= even LOWER QUARTILE (Q1)= th OBSERVATION UPPER QUARTILE (Q3)= OBSERVATION

  18. DECILES AND PERCENTILES OF UNGROUPED DATA DECILE (Dx) = IF, X=odd DECILE (Dx) = IF, X=EVEN DECILE CAN BE BETWEEN 1 AND 9 D1,D2 ………….D9 PERCENTILE (Px) = IF, X=odd PERCENTILE (Px) = IF, X=EVEN PERCENTILE CAN BE BETWEEN 1 AND 99 P1,P2 ………….P99

  19. PARTITION VALUES(Q2) OF UNGROUPED FREQUENCY DISTRIBUTION FORMAT x f <c.f x1 f1 . x2 f2 m . . . . . . xnfn . ∑fi=N FOR MEDIAN FIND AND LOOK FOR A NO. JUST GRATER THAN IN THE <c.f COLUM SAY(m) NOW, X VALUE CORRESPONDING TO m IS THE MEDIAN

  20. PARTITION VALUES(Q1) OF UNGROUPED FREQUENCY DISTRIBUTION FORMAT x f <c.f x1 f1 . x2 f2 m . . . . . . xnfn . ∑fi=N FOR LOWER QUARTILE FIND AND LOOK FOR A NO. JUST GRATER THAN IN THE <c.f COLUM SAY(m) NOW, X VALUE CORRESPONDING TO m IS THE LOWER QUARTILE

  21. PARTITION VALUES(DX) OF UNGROUPED FREQUENCY DISTRIBUTION FORMAT x f <c.f x1 f1 . x2 f2 m . . . . . . xnfn . ∑fi=N FOR DECILE XFIND AND LOOK FOR A NO. JUST GRATER THAN IN THE <c.f COLUM SAY(m) NOW, X VALUE CORRESPONDING TO m IS THE DESILE X

  22. PARTITION VALUES(PX) OF UNGROUPED FREQUENCY DISTRIBUTION FORMAT xf<c.f x1 f1 . x2 f2 m . . . . . . xnfn . ∑fi=N FOR PERCENTILE X FIND AND LOOK FOR A NO. JUST GRATER THAN IN THE <c.f COLUM SAY(m) NOW, X VALUE CORRESPONDING TO m IS THE PERCENTILR X

  23. TO FIND MEDIAN OF GROUPED FREQUENCY DISTRUBUTION FORMAT c.if<c.f 0-5 7 7 5-10 18 25 10-15 25 50 15-20 30 80 20-25 20 100 ∑f = N = 100 N=100 =50 NO. JUST GREATER THAN 50 IN c.f COLUM IS 80 MEDIAN CLASS IS 15-20 MEDIAN = L+×c.w

  24. TO FIND D4OF GROUPED FREQUENCY DISTRUBUTION FORMAT c.if<c.f 0-5 7 7 5-10 18 25 10-15 25 50 15-20 30 80 20-25 20 100 ∑f = N = 100 N=100 4 =40 NO. JUST GREATER THAN 40 IN c.f COLUM IS 50 D4CLASS IS 10-15 D4= L+ ×c.w

  25. TO FIND P21OF GROUPED FREQUENCY DISTRUBUTION FORMAT c.if<c.f 0-5 7 7 5-10 18 25 10-15 25 50 15-20 30 80 20-25 20 100 ∑f = N = 100 N=100 21=21 NO. JUST GREATER THAN 21 IN c.f COLUM IS 25 P21CLASS IS 5-10 P21= L+ ×c.w

  26. TO FIND THE MODE • TO FIND THE MODE OF UNGROUPED DATA JUST FIND THE MAX FREQUENCY. • OBSERVATION CORRESPONDING TO THE MAX FREQUENCY IS THE MODE. • Eg. 11, 9, 2, 2, 11, 15, 9, 2, 3, 12 • THE MODE FOR ABOVE DATA IS 2.

  27. MODE FOR GROUPED FREQUENCY DATA • FOR THIS A HISTOGRAM IS REQUIRED. • ALSO, THE FOLLOWING FORMULA CAN BE USED MODE = L +

  28. Eg.

  29. TO FIND PARTITION VALUES USING OGIVE CURVES

  30. TO FIND MEDIAN USING BOTH OGIVE CURVES

  31. THANK YOU

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