The median and the quartiles you found for the IQR split data into four parts. A box plot draws them.
Idea clave
A box plot shows the five-number summary: minimum, $Q_1$, median, $Q_3$, maximum. The box runs from $Q_1$ to $Q_3$ with a line at the median, and whiskers reach out to the minimum and maximum. Each of the four sections holds about a quarter of the data.
Por qué funciona
The five numbers cut the ordered data into four groups with about the same number of values. A box plot places those cuts on a number line, so you can see the center (the median line) and the spread (the width of the box and the whiskers) at a glance. A long section means its values are spread over a wide range, not that it holds more of them.
Ejemplo resuelto: Make the summary
Find the five-number summary of 4, 6, 7, 9, 10, 12, 15, 16, 21.
- Minimum 4, maximum 21. Nine values, so the median is the 5th: 10.
- Lower half 4, 6, 7, 9: $Q_1 = (6 + 7) \div 2 = 6.5$.
- Upper half 12, 15, 16, 21: $Q_3 = (15 + 16) \div 2 = 15.5$.
Respuesta: 4, 6.5, 10, 15.5, 21
Ejemplo resuelto: Read a box plot
In a box plot, $Q_3 = 30$. About what percent of the data is above 30?
- Above $Q_3$ is the right whisker: one of the four sections.
Respuesta: About 25%
Error común
Thinking a longer section of a box plot holds more data points. In the plot above, the right whisker (15.5 to 21) is longer than the left one (4 to 6.5), but each holds about a quarter of the values. Quick check: count the dots in each section, not the length.