Stem-and-Leaf Plots

Section 1 of 2

Stem & leaf

Split each number into a stem (all but the last digit) and a leaf (the last digit). List the leaves in order beside each stem. The leaf is one digit only, and you must include a key.

Worked example — build one

Show $21, 35, 43, 28, 36, 46, 49$ on a stem-and-leaf plot.

Stems are the tens: $2, 3, 4$

see the plot — key $2\,|\,1 = 21$

2	1 8
3	5 6
4	3 6 9

Key: 2 | 1 = 21

You try

Show $135, 147, 131, 152, 147, 138, 139, 144$ on a stem-and-leaf plot.

Here the stem is the first two digits (the hundreds and tens): $13, 14, 15$. The leaf is the units.

$13\,|\,1\ 5\ 8\ 9$

$14\,|\,4\ 7\ 7$

$15\,|\,2$

key $14\,|\,7 = 147$

13	1 5 8 9
14	4 7 7
15	2

Key: 14 | 7 = 147

Section 2 of 2

Back-to-Back Stem-and-Leaf

Comparing two sets

Two sets share the same stems in the middle; one set’s leaves go to the left (read right-to-left), the other to the right. Then compare the means — a higher mean is generally better.

Worked example — compare two subjects

French: $25, 36, 43, 44, 37, 49$. German: $38, 46, 47, 39, 43, 21$. Show back-to-back and say who did better.

French mean $= \tfrac{25+36+37+43+44+49}{6} = 39$

German mean $= \tfrac{21+38+39+43+46+47}{6} = 39$

The means are equal — the two subjects are about the same

both mean $39$ — about even

French		German
5	2	1
7 6	3	8 9
9 4 3	4	3 6 7

Key: French $5\,|\,2 = 25$ · German $2\,|\,1 = 21$

That’s Class 7.

Stem-and-leaf plots (leaf = one digit, always a key) and back-to-back plots to compare two sets. Class 8: scatter plots and correlation.