## Saturday, April 9, 2005

### Quartile, Centile and Percentile

Question from RxPG - AIPG 2001 to 2005 Book by Bruno.

AIPG 2003 - Question 52.
A measure of location which divides the distribution in the ratio of 3:1 is:
1. Median.
2. First quartile.
3. Third quartile.
4. Mode.
3. Third quartile.
Reference
Methods of Biostatistics by T.Bhaskar Rao (PARAS) Page 28
High Yield Biostatistics Page 9
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High Yield Biostatistics
Discussion
The location of other points in the range can be measured by Percentiles of centiles, which are values in a series of observations, arranged in ascending order of magnitudes which divides the distribution into 100 equal parts. Median is 50th percentile. i.e. it will have 50% observations on either side, 10th percentile should have 10% observations to the left and 90% of the right. Percentiles are used to divide a distribution into convenient groups. Those in common use are:
· Quartile denotes division of the entire range of distribution into four equal parts, of equal probability by three equidistant points
o First Quartile - will have distribution in the ratio = 1:3 (as 25% observations are to the left and 75% to the right)
o Second Quartile - will have distribution in ratio = 2:2 (or 1:1 , as 50% observations are to the left and 50% to the right)
o Third Quartile - will have distribution in the ratio= 3:1 (as 75% of observations are to left and 25% to the right)
· Quintiles: Four in number, divide the distribution into five equal parts.
o So 20th percentile or first quintile will have 20% observations falling on its left and 80% to its right.
· Deciles: Nine in number, divide the distribution into 10 equal parts.
o First decile or 10th percentile will have 10% observations on its left and 90% to its right 5th decile will be same as median.
Explanation
1. Median is the middle value, when all the values are arranged either in ascending or descending order.
2. First quartile will have distribution in the ratio = 1:3 (as 25% observations are to the left and 75% to the right).
3. Third quartile will have distribution in the ratio= 3:1 (as 75% of observations are to left and 25% to the right).
4. Mode is the most commonly occuring value.
Centiles are commonly used in Growth Charts (see the chapter Preventive Medicine is OG and Paediatrics)
Tips
Quartile has 4 parts
and 3 points. Quintiles will have 5 parts and 4 points and so on. The number of points will be one less than the number of parts. The “root” in the terminology refers to the “paRts” and not the points. That means if some one asks you about how many points will be there in an Octile, don’t jump to say 8. Octiles have 8 parts and 7 points

Percentile is very simple to understand..............

A rank list is prepared.......... and then Your percentile can be calculated by
Percentile=(Total candidates - Your Rank)/Total Candidates x 100

There are other similar but slightly different methods

For example there are 1000 candidates
You got a rank of 1. Your percentile is 99.9
You got a rank of 500. Your percentile is 50
You got a rank of 250. Your percentile is 75

For example when there are 3567 candidates
You get Rank 1. your percentile is 3566/35.67=99.971
You get Rank 100. Your percentile is 3467/35.67=97.19
You get Rank 1784. Your percentile is 49.98