Minimum, lower quartile ($Q_1$), median ($Q_2$), upper quartile ($Q_3$), maximum. The box runs from $Q_1$ to $Q_3$ (its width is the interquartile range, $\text{IQR}=Q_3-Q_1$), the median is marked inside it, and whiskers stretch out to the minimum and maximum. Each of the four sections — below $Q_1$, $Q_1$–$Q_2$, $Q_2$–$Q_3$, above $Q_3$ — holds exactly 25% of the data.

Order the data first — always. Find the median, then take the median of each half separately: the lower half gives $Q_1$, the upper half gives $Q_3$.

Odd $n$ (7 values: 4,6,10,11,15,17,19): median is the 4th value, $11$ — and it's excluded from both halves. Lower half $\{4,6,10\}\Rightarrow Q_1=6$; upper half $\{15,17,19\}\Rightarrow Q_3=17$.

Even $n$ (8 values: 22,25,28,31,35,38,40,42): median $=\frac{31+35}{2}=33$; the data splits cleanly with nothing excluded. Lower half $\{22,25,28,31\}\Rightarrow Q_1=\frac{25+28}{2}=26.5$; upper half $\{35,38,40,42\}\Rightarrow Q_3=39$.

Same logic as estimating a median from cumulative frequency, run three times. Find $\frac{N}{4}$, $\frac{N}{2}$, $\frac{3N}{4}$ on the y-axis, read across to the curve and down to the x-axis for $Q_1$, $Q_2$, $Q_3$. The minimum and maximum are simply where the curve starts and ends.

$N=120$: positions $30$, $60$, $90$ give (say) $Q_1=35$, median$=42$, $Q_3=51$; if the curve runs from $20$ to $70$, those are the min/max. Five-number summary: $\{20, 35, 42, 51, 70\}$.

Never just list values from each plot — that scores poorly. Always compare two things, in context: the median (which group did better on average) and the IQR (which group was more consistent).

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Use the $1.5\times\text{IQR}$ rule to define fences beyond which a point counts as a statistical outlier:

Any value outside these fences is plotted as a separate point (a cross or dot); the whisker itself then only extends to the last non-outlier value, not all the way to the true minimum/maximum.

Company A's commute times (min): $Q_1=22$, median$=31$, $Q_3=40$. Company B's: $Q_1=18$, median$=25$, $Q_3=48$. Compare the two distributions.

1. Medians: Company A ($31$) has a longer typical commute than Company B ($25$).
2. IQRs: $\text{IQR}_A = 40-22=18$; $\text{IQR}_B=48-18=30$.
3. Company A's commute times are more consistent (smaller IQR of 18) than Company B's (wider IQR of 30), even though Company A's typical commute is longer.

Notice the two findings can point in different directions — always report both the average and the spread, since a question can ask to compare them separately.