The document discusses percentiles and how they are used to divide a distribution of data into 100 equal parts. It provides examples of calculating percentiles for both continuous and discrete data series, explaining how to determine the item size corresponding to a given percentile based on the cumulative frequency, median class limits, and size of the dividing portion. The 70th percentile of a sample data set is calculated as an example for a continuous series.

1. Percentiles
Suresh Babu G
Assistant Professor
CTE CPAS Paippad, Kottayam

2. Percentiles
• Percentiles divide the distribution into 100 equal
parts.
• We get 99 dividing portions denoted by P1, P2,
P3, ……., P99.
• P50 is the median.
100
)1( NX
Px = Size
th
Item
X = dividing portion number

3. Individual Series
Example : The following data provides marks of
seven students. Calculate 70 th Percentile
110, 115, 140, 117, 109, 113, 120
Arrange the data in ascending order
109, 110, 113, 115, 117, 120, 140
P70 = Size of item
P70 = Size of item = Size of item
P70 = Size of 5.6 item = 117 + (0.6 x 3)
= 117 + 1.8 = 118.8 P70 = 118.8
100
)1(70 N
100
)17(70 
100
560
th
th th
th

4. Discrete Series
PX = Size of item
Example:
Calculate P60
100
)1( NX th
Marks No: of students
10 2
20 4
30 10
40 4

5. P60 = Size of item
P60 = Size of item = Size of
item
Median = Size of 12.6 item
12.6 is easily located at 16 of cf corresponding
mark is 30 so P60 = 30
Marks No: of students Cumulative
Frequency
10 2 2
20 4 6
30 10 16
40 4 20
100
)1(60 N th
100
)120(60 
th
100
1260
th
th

6. Continues Series
Px =
Where L = Lower limit of the median class
cf = Cumulative frequency of the
classes preceding the median class
f = frequency of the median class
h = magnitude of the median class
interval
X = dividing portion number
h
f
cfNX
L 


)100/(

7. Example: Find P30
Marks No of Students
0 – 10 4
10 – 20 12
20 – 30 24
30 – 40 36
40 – 50 20
50 – 60 16
60 – 70 8
70 - 80 5

8. P30 =
P30 = 20 + 8.96 = 28.96
P30 = 28.96
Marks No of
Students
Cumulative
Frequency
0 – 10 4 4
10 – 20 12 16
20 – 30 24 40
30 – 40 36 76
40 – 50 20 96
50 – 60 16 112
60 – 70 8 120
70 - 80 5 125
Size of 30N/100 th item
= Size of 30x125/100 th
item
= Size of 37.5 th item
Median class = 20 – 30
L = 20
cf = 16
f = 24
h = 10
h
f
cfN
L 


)100/(30
P30 =
10
24
16)100/125(30
20 


10
24
5.2120 

9. Try to do more
exercise