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.**Answer**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.

**Comments**

Centiles are commonly used in Growth Charts (see the chapter Preventive Medicine is OG and Paediatrics)

**Tips**

and 3 points.

__Quart__ile has 4 parts**and 4 points and so on. The number of points will be one less than the number of parts. The “**

__Quint__iles will have 5 parts**oot” in the terminology refers to the “pa**

__r__**ts” 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.**

__R__

__Oct__iles have 8 parts and 7 pointsPercentile 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

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