Percentiles — Meaning and Computation for Individual, Discrete and Continuous Series

Percentiles divide an ordered series into a hundred equal parts, giving ninety-nine percentiles $P_1$ through $P_{99}$. $P_i$ marks the point below which $i\%$ of the observations lie — this is the finest-grained partition value studied in the MSBSHSE Std XI Economics syllabus, and the one used whenever a very precise relative rank (such as an entrance-exam 'percentile score') must be reported.

Individual series. Locate the position $k=iN/100$ for $P_i$ ($i=1,\ldots,99$), using the identical rounding/averaging rule already used for quartiles and deciles.

Discrete series. Build the cumulative frequency column; locate $k=iN/100$; the percentile is the value of X at the first class whose cf equals or just exceeds $k$.

Continuous (grouped) series. Locate the percentile class — the class whose cf first equals or exceeds $k=iN/100$ — then interpolate:

$P_i = L + \frac{\frac{iN}{100}-cf}{f}\times h$ …