MEAN MEDIAN AND PARTITION VALUES MEAN DEFINETION OF

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. �

TO FIND THE MEAN OF UNGROUPED FREQUENCY DISTRIBUTION FORMAT : MEAN x x 1 x 2 x 3 . . x n f f 1 f 2 f 3 . . fn fx f 1 x 1 f 2 x 2 f 3 x 3. . f n xn ∑fixi x = ∑fixi/∑fi

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

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

TO FIND THE MEAN WHEN CF IS GIVEN FORMAT 1 MARKS below 10 below 20 below 30 below 40 below 50 C. I 0 -10 10 -20 20 -30 30 -40 40 -50 USE X= ∑fixi/∑fi NO. OF STUDENTS(c. f) 5 9 17 29 45 f 5 4 8 12 16 ∑f f 5 -0 9 -5 17 -9 29 -17 45 -29 x 5 15 25 35 45 =5 =4 =8 = 12 = 16 fx 25 60 200 420 720 ∑fx

TO FIND THE MEAN WHEN CF IS GIVEN FORMAT 2 marks above 50 above 60 above 70 above 80 above 90 above 100 no. of students(c. f) 36 31 21 18 7 0 C. I 50 -60 60 -70 70 -80 80 -90 90 -100 f 5 10 3 11 7 ∑f MEAN x =∑fx/∑f f 5 10 3 11 7 0 x 55 65 75 85 95 fx 275 650 225 935 665 ∑fx

CHANGE IN A MEAN IF a IS ADDED, SUBTRACTED MULTIPLIED OR DIVIDED TO EACH OBSERVATION THE MEAN CHANGES ACCORDINGLY ie, a IS ADDED, SUBTRACTED MULTIPLIED OR DIVIDED TO THE MEAN eg. X 1, X 2 ……………. Xn X 1+a, X 2+a…………. . Xn+a X= x 1+x 2+……………. xn X= X+a n Eg. 1, 2, 3, 4, 5, 6 X= 3. 5 1+1, 2+1, 3+1, 4+1, 5+1, 6+1 X= 3. 5+1 =4. 5

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

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

COMBINED MEAN LET, n 1 AND n 2 BE THE NO OF OBJECTS IN TWO GROUPS, LET, X 1 AND X 2 BE THE MEAN OF THE TWO GROUPS THEN THE COMBINED MEAN OF BOTH THE GROUPS IS GIVEN BY, X = n 1 x 1+n 2 x 1/n 1+n 2

MEDIAN AND OTHER PARTITION VALUES

MEDIAN FOR UNGROUPED DATA �

MEDIAN FOR UNGROUPED DATA �

LOWER AND UPPER QUARTILE OF UNGROUPED DATA �

DECILES AND PERCENTILES OF UNGROUPED DATA �

PARTITION VALUES(Q 2) OF UNGROUPED FREQUENCY DISTRIBUTION �

PARTITION VALUES(Q 1) OF UNGROUPED FREQUENCY DISTRIBUTION �

PARTITION VALUES(DX) OF UNGROUPED FREQUENCY DISTRIBUTION �

PARTITION VALUES(PX) OF UNGROUPED FREQUENCY DISTRIBUTION �

TO FIND MEDIAN OF GROUPED FREQUENCY DISTRUBUTION �

TO FIND D 4 OF GROUPED FREQUENCY DISTRUBUTION �

TO FIND P 21 OF GROUPED FREQUENCY DISTRUBUTION �

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.

MODE FOR GROUPED FREQUENCY DATA �

Eg.

TO FIND PARTITION VALUES USING OGIVE CURVES

TO FIND MEDIAN USING BOTH OGIVE CURVES

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