Quantiles, box plots and their uses

In short

• Quartiles split sorted data into 4 equal parts, quintiles into 5, deciles into 10 and percentiles into 100. The median is Q2, the 5th decile and the 50th percentile.
• In raw data the y-th percentile sits at position $L_y = (n+1)\,y/100$; interpolate when the position is not a whole number.
• The interquartile range IQR = Q3 − Q1 covers the middle 50% of the data and ignores extremes.
• A box-and-whisker plot draws the IQR as a box with the median inside, and whiskers out to the extremes or to fences 1.5 × IQR beyond the box.
• Investors use quantiles to rank managers against peers and to sort stocks into groups, such as size deciles, for research.