Percentiles are positional measures used to indicate an individual's position within a group. They divide a data set into 100 equal parts, with percentiles (denoted Px) indicating what percent of values are less than a specified value. Common percentiles include the median (P50), quartiles (P25, P50, P75), and deciles. Percentiles are calculated using a formula that determines the position number based on the total number of data points and percentile value. This position is then used to find the corresponding value within ordered data.

1. Percentiles

2. Percentiles are positional measures used mainly in
educational and health-related fields to indicate the
position of an individual in a group.
For example, the graphs and tables show the
percentiles for various measures such as test scores,
height or weight.

3. Percentiles (denoted
Px) divide a set of data
into 100 equal parts.
They are used as
positional measures
to indicate what
percent of the data
set have a value less
than a specified value.
Percentiles are not the same as percentages.
For example, if a student gets 72 correct
answers out of 100 on a test they earn 72%.
If a score of 72 correct answers corresponds to
the 64th percentile, then they did better than
64% of the students in the class, but still
received a score of 72%.
80% of the people are
shorter than “you”

4. Special Cases
•The median is the value that is
in the halfway position of a
data set. Median = P50
•The quartiles are the values
that are in the quarter
positions of a data set.
First Quartile = Q1 = P25
Third Quartile = Q2 = P75
•The deciles are the values that
are in the positions that
divided the data into 10 pieces.
D1 = P10
D2 = P20
…
D10 = P100
Some frequently used percentiles have specific names:

5. Formula
Provided data is ordered least to
greatest, the position number of
the percentiles can be calculated
using the formula:
With percentiles, there are two items
of interest:
1. the position of the percentile
(found using the formula), and
2. the value of the percentile (for
example, P50 = 139, means the 50th
percentile has a value
 
1
Position number of P
100
x
n
x



6. Calculating Percentiles
The following data lists the
number of calories in 22
manufactures vanilla-flavoured
ice cream bars.
Given the data above
determine:
a) the median
b) the first quartile
c) the third quartiles
d) the fourth decile

7. Calculating Percentiles
a) the median
 50
22 1
Position number of P 50
100
11.5



 
 
th th th
50P 11 value + 0.5 12 value -11 value
209 0.5 234 209
221.5

  

11th & 12th
positions

8. Calculating Percentiles
b) the first quartile
 25
22 1
Position number of P 25
100
5.75



 
 
th th th
25P 5 value + 0.75 6 value -5 value
151 0.75 179 151
172

  

5th & 6th
positions

9. Calculating Percentiles
c) the third quartile
 75
22 1
Position number of P 75
100
17.25



 
 
th th th
75P 17 value + 0.25 18 value -17 value
319 0.25 337 319
323.5

  

17th & 18th
positions

10. Calculating Percentiles
d) the fourth decile
 40
22 1
Position number of P 40
100
9.2



 
 
th th th
40P 9 value + 0.2 10 value -9 value
197 0.2 201 197
197.8

  

9th & 10th
positions