Suppose n = 22 = 5(4) + 2. Computing the first quartile as defined using the "n+1" approach gives
\begin{equation*}
(n+1)s = 23(0.25) = 5.75 = 5 + 0.75 = m + r.
\end{equation*}
Therefore,
\begin{equation*}
Q_1 = 0.25 \times y_5 + 0.75 \times y_6
\end{equation*}
which is a value closer to \(y_6\text{.}\) Using the "n-1" approach gives
\begin{equation*}
(n-1)s+1 = 21(0.25)+1 = 5.25 = 5 + 0.25 = m + r.
\end{equation*}
Therefore,
\begin{equation*}
Q_1 = 0.75 \times y_5 + 0.25 \times y_6
\end{equation*}
which is a value closer to \(y_5\text{.}\)