mean,median and partition values
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
MEAN,MEDIAN AND PARTITION
VALUES
MEAN
DEFINETION OF CENTRAL TENDENCYIT IS DEFINED AS THE REPRESENTATIVE OF A GIVEN DATA.SOME Eg. OF CTs ARE
MEANMEDIANMODELOWER QUARTILEUPPER QUARTILEDECILEPERCENTILE
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, 6X= = 21 = 3.5
6 6
TO FIND THE MEAN OF UNGROUPED FREQUENCY DISTRIBUTIONFORMAT :
x f fxx1 f1 f1x1
x2 f2 f2x2
x3 f3 f3x3
. . .
. . . xn fn fnxn
∑fi ∑fixi
MEAN x = ∑fixi/∑fi
TO FIND THE MEAN OF GROUPED FREQUENCY DISTRUBUTION(WHERE CI IS NON-CONTINUOUS)
FORMAT :C.I f mid value(x) fx0-4 2 2 45-9 3 7 2110-14 5 12 6015-19 2 17 34 ∑fi ∑fixi
MEAN: x = ∑fixi/∑fi
TO FIND THE MEAN OF GROUPED FREQUENCY DISTRUBUTION(WHERE CI IS CONTINUOUS)FORMAT :
C.I f mid 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
TO FIND THE MEAN WHEN CF IS GIVENFORMAT 1
MARKS NO. OF STUDENTS(c.f) fbelow 10 5 5-0 = 5below 20 9 9-5 = 4below 30 17 17-9 = 8below 40 29 29-17 = 12below 50 45 45-29 = 16
C.I f x fx0-10 5 5 2510-20 4 15 6020-30 8 25 20030-40 12 35 42040-50 16 45 720∑f ∑fxUSE X= ∑fixi/∑fi
TO FIND THE MEAN WHEN CF IS GIVEN
FORMAT 2marks no. of students(c.f) fabove 50 36 5above 60 31 10above 70 21 3above 80 18 11above 90 7 7above 100 0 0 C.I f x fx50-60 5 55 27560-70 10 65 65070-80 3 75 22580-90 11 85 93590-100 7 95 665∑f ∑fx
MEAN x =∑fx/∑f
CHANGE IN A MEANIF 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 MEANeg. X1, X2 ……………………….Xn X1+a,X2+a…………..Xn+a
X= x1+x2+……………………….xn X= X+a
nEg.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
MEAN BY SHORTCUT METHODFORMAT
c.i f mid 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
MEAN BY STEP DEVIATION METHOD
FORMATc.i f mid 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 1
8 40-50 10 45 2
20∑fi
∑fidi
USE MEAN x = A+ h(∑fidi/ ∑fi)
COMBINED MEANLET, 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
MEDIAN AND OTHER
PARTITION VALUES
MEDIAN FOR UNGROUPED DATAFORMAT 1
X1, X2, X3……………………………Xnn= 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). )= 5th OBSERVATION AFTER ARRENGING IN ASCENDING/DESCENDING ORDER
1 1 2 3 3 4 5 5 6 5TH OBSERVATION
MEDIAN = 3
MEDIAN FOR UNGROUPED DATAFORMAT 2
IF n=EVENFIND THE VALUE OF th OBSERVATION AFTER
ARRANGING IN ASCENDING/DESCENDING ORDER. THE MEAN OF th AND THE NEXT OBSERVATION GIVES YOU THE MEDIANEg. 1 2 1 3 4 5 n=6
1 1 2 3 4 5 = 3rd OBSERVATION MEDIAN = = 2.5
LOWER AND UPPER QUARTILE OF UNGROUPED DATA
IF n = odd LOWER QUARTILE (Q1)= th OBSERVATIONUPPER QUARTILE (Q3)= OBSERVATIONIF n= evenLOWER QUARTILE (Q1)= th OBSERVATIONUPPER QUARTILE (Q3)= OBSERVATION
DECILES AND PERCENTILES OF UNGROUPED DATADECILE (Dx) = IF, X=oddDECILE (Dx) = IF, X=EVEN
DECILE CAN BE BETWEEN 1 AND 9D1,D2 ………….D9
PERCENTILE (Px) = IF, X=oddPERCENTILE (Px) = IF, X=EVEN
PERCENTILE CAN BE BETWEEN 1 AND 99P1,P2 ………….P99
PARTITION VALUES(Q2) OF UNGROUPED FREQUENCY DISTRIBUTIONFORMAT
x f <c.fx1 f1 .
x2 f2 m. . .. . .xn fn .
∑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
PARTITION VALUES(Q1) OF UNGROUPED FREQUENCY DISTRIBUTION
FORMATx f <c.fx1 f1 .
x2 f2 m. . .. . .xn fn .
∑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
PARTITION VALUES(DX) OF UNGROUPED FREQUENCY DISTRIBUTION
FORMATx f <c.fx1 f1 .
x2 f2 m. . .. . .xn fn .
∑fi=N
FOR DECILE 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 DESILE X
PARTITION VALUES(PX) OF UNGROUPED FREQUENCY DISTRIBUTIONFORMAT
x f <c.fx1 f1 .
x2 f2 m. . .. . .xn fn .
∑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
TO FIND MEDIAN OF GROUPED FREQUENCY DISTRUBUTION
FORMAT c.i f <c.f 0-5 7 7 5-10 18 2510-15 25 5015-20 30 8020-25 20 100
∑f = N = 100N=100 =50
NO. JUST GREATER THAN 50 IN c.f COLUM IS 80MEDIAN CLASS IS 15-20
MEDIAN = L+ ×c.w
TO FIND D4 OF GROUPED FREQUENCY DISTRUBUTION
FORMAT c.i f <c.f 0-5 7 7 5-10 18 2510-15 25 5015-20 30 8020-25 20 100 ∑f = N = 100N=100 4 =40
NO. JUST GREATER THAN 40 IN c.f COLUM IS 50D4 CLASS IS 10-15D4 = L+ ×c.w
TO FIND P21 OF GROUPED FREQUENCY DISTRUBUTIONFORMAT
c.i f <c.f 0-5 7 7 5-10 18 2510-15 25 5015-20 30 8020-25 20 100
∑f = N = 100N=100 21=21
NO. JUST GREATER THAN 21 IN c.f COLUM IS 25P21 CLASS IS 5-10
P21 = L+ ×c.w
TO FIND THE MODETO 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, 12THE MODE FOR ABOVE DATA IS 2.
MODE FOR GROUPED FREQUENCY DATAFOR THIS A HISTOGRAM IS REQUIRED.ALSO, THE FOLLOWING FORMULA CAN BE USED
MODE = L +
Eg.
TO FIND PARTITION VALUES USING OGIVE CURVES
TO FIND MEDIAN USING BOTH OGIVE CURVES
THANK YOU