Interpretation and Relationships

What Each Value Says

• $Q_1$ (first quartile): about 25% of the observations lie below it (and 75% above).
• $Q_3$ (third quartile): about 75% of the observations lie below it (and 25% above).
• $D_j$ (the $j$-th decile): about $10j\%$ of the observations lie below it — e.g. $D_7$ has roughly $70\%$ below.
• $P_k$ (the $k$-th percentile): about $k\%$ of the observations lie below it — e.g. $P_{80}$ has roughly $80\%$ below.

Relationships Among the Families

Because all three families partition the same ordered data, many partition values coincide:

$Q_1 = P_{25}, \qquad Q_2 = D_5 = P_{50} = \text{Median}, \qquad Q_3 = P_{75},$

and every decile is a percentile: $D_j = P_{10j}$ (for example $D_3 = P_{30}$, $D_7 = P_{70}$).

A Preview — Spread via Quartiles …