Quartiles

Ok the following list of data is:

0, 0, 1, 2, 2, 5, 6, 6, 8, 10

Median 3.5

Q1 -- Is it 0.5 or 1? If it is 1, 25% of the observations are not at or below this value.???? However if I take the first half of the data: 0, 0, 1, 2, 2, then 1 is clearly the middle of this data and as such Q1

Q3 -- is it 6 or 7? Same issue

Please clarify for me.

Thanks

There is no universal agreement on how to estimate quartiles, especially from small samples. Either of your proposed methods is acceptable. Check with your instructor.

Royhass has it right. Maybe a conjecture can help clarify your question. For your data, suppose there are ten entries for each of the data points you list. For instance there are 10 zeros, another 10 zeros, ten ones, ten twos, another 10 twos, etc. There are a total of 100 data points. The median is still 3.5. The 1st quartile is clearly 1. Twenty zeros and five of the ten ones lie at or below the 25th percentile. The other 5 ones, lie above the 1st quartile.