The above two diagrams show you how to find the 1st quartile, median (2nd Quartile) and the 3rd quartile of ungroup data.

 

In the diagram (Data Set 1), there are a total of 15 numbers,  the median value is in the (15+1)/2 = 8th position, number 10.

To find the 1st quartile, locate the number between the 1st  position and the 8th position (median), which is the 4th position, number  4.

To find the 3rd quartile, locate the number between the last position (15th)  and the 8th position (median), which is the 12th position, number 19.

 

In the diagram (Data Set 2), there are a total of 14 numbers,  the median value is in the (14+1)/2 = 7.5th position, as there is no such thing as a 7.5th position

we will take the numbers of the 7th position (11) and 8th position (13), and average the two numbers (11+13)/2 = 12.

To find the 1st quartile, locate the number between the 1st  position and the 7th position , which is 4th position, number  7. .

To find the 3rd quartile, locate the number between the last position (15th)  and the 8th position, which is 12th position, number 16.

 

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