Posted by **Denim** on Sunday, March 4, 2007 at 11:44am.

How do I Find the first and third quartiles, Q1 and Q3, of the following set of numbers?

13,4,12,16,8,14,8,3,10,8

order the data:

3,4,8,8,8,10,12,13,14,16

Quartile I ends at 8

The quartile II ends at 9.

quartile III ends at 13

**
**

The calculation of the quartiles is sometimes not quite clear (especially if the number of observations of a sample is not divisible by four). We therefore provide exact instructions how to calculate the quartiles. Assuming a sample of N observations the quartiles are defined as follows ("round" stands for the rounding to the nearest integer):

1. quartile: the value of the sorted series of observations having the position x = round(0.25*(N+1))

2. quartile (median): if N is even, Q2 is the mean of the two values at the positions N/2 and N/2+1; if N is odd, Q2 is the value at the position (N+1)/2

3. quartile: the value of the sorted series having the position x = round(0.75*(N+1))

Example:
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