Different results: Quartiles and BoxWhiskerChart vs. Quantiles?

Questions
,
1

Why does the functions Quartiles and BoxWhiskerChart deliver results others than Quantiles?
See attached file. Thx. for answers!

demo.nb (9.25 KB)

2

Quartiles returns:

Quantile[list,{1/4,1/2,3/4},{{1/2,0},{0,1}}

Where the first number is different from:

Quantile[list,1/4]

Look under details & options in the Quartiles documentation.