I am having some troubles understanding what the components of a box and whiskers plot mean.
Let's say I have some observations.
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
This is an even number of observations and the median will be $5.5$. The lower quartile will be $3$ and the upper quartile will be $7.5$. According to my textbook, the quartiles divide the statistical material into 4 equally big parts. I can accept that as long as the quartiles are not part of the observations anymore, because otherwise you cannot split 10 into 4 parts with only whole numbers.
Once you have determined what the quartiles are, are the quartile values still part of the observations? Because if yes, I don´t understand how the lower quartile can split the data set into four equally big parts.