Presentation on theme: "PARTITION VALUES-QUARTILES,DECILES AND PERCENTILES"— Presentation transcript:
1PARTITION VALUES-QUARTILES,DECILES AND PERCENTILES 1.QUARTILES: Quartiles divides a series into 4 equal parts. For any series there are three quartiles denoted by Q1,Q2 and Q3. Q1 is known as first or lower quartile, covering 25% items. The second quartile or Q2 is the same as Median of the series. Q3 is called third or upper quartile, covering 75% items.2.Deciles: Deciles divides a series into 10 equal parts. For any series, there are 9 deciles denoted by D1,D2…D9. These are called as first decile, second decile so on.3.Percentiles: Percentiles divide a series into 100 equal parts. For any series, there are 99 percentiles denoted by P1,P2,P3…P99.
2Calculation of Quartiles, Deciles and Percentiles For Individual and Discrete SeriesQ1= Size of N+1/4th itemQ3= Size of 3(N+1)/4th itemD1= Size of N+1/10th itemD9 = Size of9(N+1)/10th itemP1= Size of N+1/100th itemP99= Size of 99(N+1)/100th item
3Calculation of Quartiles, Deciles and Percentiles For Continuous SeriesQ1=Size of N/4th itemQ3 =Size of 3N/4th itemD1=Size of N/10th itemD9=Size of 9N/10 itemP1 =Size of N/100th itemP99=Size of 99N/100th itemFormula to be used in continuous series:Q1=L1+N/4-c.f*i/fQ3=L1+3N/4-c.f*i/fD1=L1+N/10-c.f*i/fD9=L1+9N/10-c.f*i/fP1=L1+N/100-c.f*i/fP99=L1+99N/100-c.f*i/f
4INDIVIDUAL SERIESExample: From the following data calculate Q1,Q3,D5 and P2521,15,40,30,26,45,50,54,60,65,70The data is first arranged in ascending order:Q1=Size of (N+1)/4th item= Size of (11+1)/4th item=Size of 3rd item=26,Q1=26Q3 =size of 3(n+1)/4th item =size of3(11+1)/4th item=size of 9th item = 60, Q3=60D5=size of 5(N+1)/10th item =size of 5(11+1)/10th item =size of 6th item=45, D5=45P25=size of 25(N+1)/100th item=size of 25(11+1)/100th item=size of 3rd item =26, P25=26sn1234567891011N=11X1521263040455054606570
5DISCRETE SERIESCalculate Q1,Q3,D6 and P85 from the following data: Q1=size of N+1/4th item=49+1/4=size of 12.5th item=13 Q3 =size of #(N+1)/4th item=3(49+1)/4=size of 37.5th item=15 D6=size of 6(N+1)/10th item=6(49+1)/10=size of 30th item=14 P85=size of 85(N+1)/100th item=85(49+1)/100=size of 42.5th item=16 Thus,Q1=13,3=15,D6=14,P85=16X101112131415161718F345721N=49C.F243441464849
6CONTINUOUS SERIESCalculation of Q1,Q3,D8 andP56 from the following data:Q1=size of N/4th item=size of 160/4th item=size of 40th itemQ1 lies in the class 10-20Q1=l1+N/4-c.f*i/f/38*10= =14.74Q1=14.74Q3 =size of 3N/4th item=3(160)/4th item=size of 120th itemQ3 lies in the class 30-40Q3=l1+3N/4-c.f*i/f/35*10=34 Q3=34D8 size of 8N/10th item=size of 8(160)/10th item=size of 128th itemD8lies in the class 30-40D8=l1+8N/10-c.f*i/f/35*10=36.29 D8=36.29P56=size of 56N/100th item 56(160)/100th itemSize of 89.6th itemP56 lies in the class20-30P56=l1+56N/100-c.f*i/f/46*10=26.43P56=26.43wages0-1010-2020-3030-4040-50f2238463519N=160c.f60106141160