Stemplot

A stemplot splits each value into a stem, the leading place values, and a leaf, the final digit. Stems run down the left in increasing order and the leaves sit beside their stem, also in increasing order. Each row behaves like a sideways histogram bar whose bin width is set by the stem unit, except that the plot keeps every original value, so the data can be read straight back out.

Eleven test scores, 52, 55, 58, 61, 63, 63, 67, 68, 72, 74 and 81, give stems by tens: 5 with leaves 2, 5, 8; 6 with leaves 1, 3, 3, 7, 8; 7 with leaves 2, 4; and 8 with leaf 1. With $n = 11$ the median is the 6th value. Stem 5 holds three leaves, so the 6th value is the third leaf on stem 6, which is 63.

That counting works only on a sorted plot. Write stem 6's leaves in the order the scores arrived, 8, 3, 7, 1, 3, and the 6th value from the top is still the third leaf on stem 6, which is now 7, so counting returns a median of 67 instead of 63. Sorting the leaves within each row is what makes the count valid; it is not a tidiness step.

What a stemplot conceals is magnitude. Stem 6 with leaf 3 means 63 only because the key says so, and the identical picture reads as 6.3 or 630 under a different key, so a stemplot with no stated key cannot be read at all. The shape is hostage to the stem unit as well. Split each stem here into low leaves 0 to 4 and high leaves 5 to 9 and those eleven scores fill seven rows instead of four, one of them empty, exposing a gap between 74 and 81 that the four-row version buried.

Stemplots are one of the three displays in topic 1.5, Graphical Representations for One Quantitative Variable.