For the sample y: 2 3 4 4 6 6 7 8 9 11

 

What is the first and third quartile?

 

My notes say it's 4 and 8.25 respectively, but my brother says it's 4 and 8.

I think your brother is correct

4 and 8 are the correct answers

 

Firstly you need to split the set into 2

2 3 4 4 6

6 7 8 9 11

 

You then take the middle value of these two sets. If I remember correctly this is not perfect.

There is no standard for this concept of "quartiles". The first quartile is simply the 25th percentile with the third quartile being the 75th percentile. Statisticians seem undecided over whether the quartile mark must be a data point or something inbetween. This is supported by the fact that if you ask for the third quartile (for example) using your TI-83 vs Casio 9800FX vs Excel spreadsheet, you will find that you get different answers. I think it's just most important to understand what it signifies rather than this formality. If it's for homework, then better ask about your teacher's preference.

There are two ways that one can compute quartiles. The standard way uses interpolation approach to evaluate a quartile, which is typical with a continuous data; But one can avoid using interpolation and find the quartiles; the later approach is used in nominal or discrete data.

 

Both the answers are correct in the above problem.