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

Deciles divide an ordered series into ten equal parts, giving nine deciles $D_1$ through $D_9$. $D_i$ marks the point below which $i$ tenths (i.e., $10i\%$) of the observations lie — $D_1$ is the 10% point, $D_5$ is the 50% point (the median, exactly), $D_9$ is the 90% point.

Individual series. Locate the position $k=iN/10$ for $D_i$ ($i=1,\ldots,9$). The same rule used for quartiles applies: if $k$ is not a whole number, round UP and take that item's value; if $k$ is a whole number, average the item at that position with the next item.

Discrete series. Build the cumulative frequency column; locate $k=iN/10$; the decile is the value of X at the first class whose cf is equal to or just greater than $k$.

Continuous (grouped) series. Locate the decile class — the class whose cf first equals or exceeds $k=iN/10$ — then interpolate:

$D_i = L + \frac{\frac{iN}{10}-cf}{f}\times h$ …