So I was trying to compute the quantiles from a dataset in R:
using the quantile() function, and I realised that it was returning unexpected quartile values for Q1 and Q3 (7 and 14, respectively, should be 6 and 16) on it's own. So I went into the documentation and saw you can assign a type to the function 1-9 that correspond to algorithms. By process of elimination type 6 yields the expected quantiles for that specific dataset, but due to my weak maths I don't actually understand the algorithms being used, and why type 6 specifically worked on my data type (more on those). Does a good explanation for when to use each type exist for someone really new to stats?