All skills Math

Learn Index · Data Management and Statistics Grade 9–10

Stem-and-leaf plots

A display where the stem is the leading digit(s) and the leaf is the last digit.

Read

Keeping every value

A stem-and-leaf plot organizes numbers while keeping every data value visible. Each number is split into:

  • a stem: the leading digit(s)
  • a leaf: the last digit

Making one

Data: test scores 62, 67, 71, 74, 74, 78, 81, 83, 85, 85, 89, 90, 94

Stem Leaves
6 2 7
7 1 4 4 8
8 1 3 5 5 9
9 0 4

Key: 7 | 4 means 74

Steps:

  1. Choose stems (here, the tens digits).
  2. Write each leaf next to its stem.
  3. Put leaves in order from smallest to largest.
  4. Add a key.

Reading the plot

  • Minimum: 62; maximum: 94; range: 32
  • Mode: 74 and 85 (both appear twice)
  • Median: 13 values → 7th value = 81
  • Shape: most scores are in the 70s and 80s.

Advantages

  • Shows the distribution like a sideways histogram.
  • Keeps the original values, so you can calculate the mean, median and mode exactly.
  • Quick to make by hand for small data sets.

Decimals and larger numbers

Use the key to show place value.

  • Heights in metres: 1 | 6 means 1.6 m
  • Times: 12 | 3 means 12.3 s
  • Large numbers: 24 | 5 means 245

Split stems

When leaves crowd onto a few stems, split each stem in two: one for leaves 0–4 and one for 5–9.

Stem Leaves
7 1 4 4
7 8
8 1 3
8 5 5 9

Back-to-back plots

A back-to-back stem-and-leaf plot compares two groups. Leaves for one group go left (read right to left), the other right.

Class A leaves Stem Class B leaves
8 5 6 2
9 4 1 7 3 5
6 2 8 0 4 7 8
9 1 5

Key: 5 | 6 | 2 means 65 for Class A and 62 for Class B.

Class B’s scores are higher overall.

Worked examples

Example 1: What value is 5 | 8 if the key says 5 | 8 = 58? 58.

Example 2: Data: 23, 31, 35, 38, 42. Make the stems. 2, 3, 4.

Example 3: Median of leaves 3 | 1 4 6 and 4 | 0 2 (values 31, 34, 36, 40, 42)? 36.

Common mistakes

  • Leaves not in order.
  • Forgetting the key.
  • Skipping a stem with no leaves: include it, so gaps in the data show.

Try it yourself

Data: 15, 22, 28, 31, 33, 33, 37, 40, 46

  1. Make a stem-and-leaf plot.
  2. Find the median.
  3. Find the mode.
  4. Find the range.

Answers: 1) 1 | 5; 2 | 2 8; 3 | 1 3 3 7; 4 | 0 6 2) 33 3) 33 4) 31

Quick recap

  • A stem-and-leaf plot splits values into stems and leaves.
  • Order the leaves and include a key.
  • Use back-to-back plots to compare two groups.