Presentation on theme: "PARTITION VALUES- QUARTILES,DECILES AND PERCENTILES 1.QUARTILES: Quartiles divides a series into 4 equal parts. For any series there are three quartiles."— Presentation transcript:
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 1.Q1= Size of N+1/4 th item 2.Q3= Size of 3(N+1)/4 th item 3.D1= Size of N+1/10 th item 4.D9 = Size of9(N+1)/10 th item 5.P1= Size of N+1/100 th item 6.P99= Size of 99(N+1)/100 th item
Calculation of Quartiles, Deciles and Percentiles For Continuous Series 1.Q 1 =Size of N/4 th item 2.Q 3 =Size of 3N/4 th item 3.D 1 =Size of N/10 th item 4.D 9 =Size of 9N/10 item 5.P 1 =Size of N/100 th item 6.P 99 =Size of 99N/100 th item Formula to be used in continuous series: 1.Q 1 =L 1 +N/4-c.f*i/f 2.Q 3 =L 1 +3N/4-c.f*i/f 3.D 1 =L 1 +N/10-c.f*i/f 4.D 9 =L 1 +9N/10-c.f*i/f 5.P 1 =L 1 +N/100-c.f*i/f 6.P 99 =L 1 +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)/4 th item= Size of (11+1)/4 th item=Size of 3 rd item=26,Q1=26 Q3 =size of 3(n+1)/4 th item =size of3(11+1)/4 th item=size of 9 th item = 60, Q3=60 D5=size of 5(N+1)/10 th item =size of 5(11+1)/10 th item =size of 6 th item=45, D5=45 P25=size of 25(N+1)/100 th item=size of 25(11+1)/100 th item=size of 3 rd item =26, P25=26 sn N= 11 X
DISCRETE SERIES Calculate Q1,Q3,D6 and P85 from the following data: Q1=size of N+1/4 th item=49+1/4=size of 12.5 th item=13 Q3 =size of #(N+1)/4 th item=3(49+1)/4=size of 37.5 th item=15 D6=size of 6(N+1)/10 th item=6(49+1)/10=size of 30 th item=14 P85=size of 85(N+1)/100 th item=85(49+1)/100=size of 42.5 th item=16 Thus,Q1=13,3=15,D6=14,P85=16 X F N=4 9 C. F
CONTINUOUS SERIES Calculation of Q1,Q3,D8 andP56 from the following data: Q1=size of N/4 th item=size of 160/4 th item=size of 40 th item Q1 lies in the class Q1=l1+N/4-c.f*i/f /38*10= =14.74 Q1=14.74 Q3 =size of 3N/4 th item=3(160)/4 th item=size of 120 th item Q3 lies in the class Q3=l1+3N/4-c.f*i/f /35*10=34 Q3=34 D8 size of 8N/10 th item=size of 8(160)/10 th item=size of 128 th item D8lies in the class D8=l1+8N/10-c.f*i/f /35*10=36.29 D8=36.29 P56=size of 56N/100 th item 56(160)/100 th item Size of 89.6 th item P56 lies in the class20-30 P56=l1+56N/100-c.f*i/f /46*10=26.43 P56=26.43 wages f N=160 c.f