Box plots
A list of numbers is hard to take in. How can five numbers summarizing it become one picture of where the data sit and how far they spread?
Where you are 3 inside
What this area is about
A box plot draws a numerical data set’s five-number summary over a number line: a box from the lower quartile Q_1 to the upper quartile Q_3, a line at the median, and whiskers out toward the extremes. Each of the four pieces holds about a quarter of the values, so the picture shows where the middle half sits and how spread out each part is, without drawing every value.
How these fit together
The basic picture. Making and reading box plots is the procedure: find the quartiles, draw the box and whiskers on a scale, then read center and spread back off the plot, including what a box plot cannot show.
A variation. Box plots that show outliers keep the same box but stop each whisker at the last value inside the fences Q_1 - 1.5\,\text{IQR} and Q_3 + 1.5\,\text{IQR}, and plot each value beyond them as its own dot.
A use. Comparing box plots puts two boxes on one shared scale to compare the center, spread and skew of two groups measured the same way.
A path through it
Quartiles and the interquartile range \text{IQR} = Q_3 - Q_1 come first. Then make and read a single box plot, and after that either the outlier version or the side-by-side comparison, in either order.
Finish here and you can compare two distributions by their centers and spreads.