PARTITION 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.

Calculation of Quartiles, Deciles and Percentiles For Individual and Discrete Series Q1= Size of N+1/4th item Q3= Size of 3(N+1)/4th item D1= Size of N+1/10th item D9 = Size of9(N+1)/10th item P1= Size of N+1/100th item P99= Size of 99(N+1)/100th item

Calculation of Quartiles, Deciles and Percentiles For Continuous Series Q1=Size of N/4th item Q3 =Size of 3N/4th item D1=Size of N/10th item D9=Size of 9N/10 item P1 =Size of N/100th item P99=Size of 99N/100th item Formula to be used in continuous series: Q1=L1+N/4-c.f*i/f Q3=L1+3N/4-c.f*i/f D1=L1+N/10-c.f*i/f D9=L1+9N/10-c.f*i/f P1=L1+N/100-c.f*i/f P99=L1+99N/100-c.f*i/f

INDIVIDUAL SERIES Example: From the following data calculate Q1,Q3,D5 and P25 21,15,40,30,26,45,50,54,60,65,70 The 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=26 Q3 =size of 3(n+1)/4th item =size of3(11+1)/4th item=size of 9th item = 60, Q3=60 D5=size of 5(N+1)/10th item =size of 5(11+1)/10th item =size of 6th item=45, D5=45 P25=size of 25(N+1)/100th item=size of 25(11+1)/100th item=size of 3rd item =26, P25=26 sn 1 2 3 4 5 6 7 8 9 10 11 N=11 X 15 21 26 30 40 45 50 54 60 65 70

DISCRETE SERIES Calculate 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=16 X 10 11 12 13 14 15 16 17 18 F 3 4 5 7 2 1 N=49 C.F 24 34 41 46 48 49

CONTINUOUS SERIES Calculation of Q1,Q3,D8 andP56 from the following data: Q1=size of N/4th item=size of 160/4th item=size of 40th item Q1 lies in the class 10-20 Q1=l1+N/4-c.f*i/f 10+40-22/38*10=10+4.74=14.74 Q1=14.74 Q3 =size of 3N/4th item=3(160)/4th item=size of 120th item Q3 lies in the class 30-40 Q3=l1+3N/4-c.f*i/f 30+120-106/35*10=34 Q3=34 D8 size of 8N/10th item=size of 8(160)/10th item=size of 128th item D8lies in the class 30-40 D8=l1+8N/10-c.f*i/f 30+128-106/35*10=36.29 D8=36.29 P56=size of 56N/100th item 56(160)/100th item Size of 89.6th item P56 lies in the class20-30 P56=l1+56N/100-c.f*i/f 20+89.6-60/46*10=26.43 P56=26.43 wages 0-10 10-20 20-30 30-40 40-50 f 22 38 46 35 19 N=160 c.f 60 106 141 160