1. 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.

2. 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

3. 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

4. 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

5. 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

6. 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
/38*10= =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
/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
/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
/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