Stem and Leaf Plots
A stem-and-leaf plot splits each value into a stem and a leaf, so the whole dataset is shown in order, grouped by tens. In NSW Year 7 maths it is used to organise and compare numerical data (NESA outcomes MA4‑DAT‑C‑01 and MA4‑DAT‑C‑02).
You will read values using the key, draw an ordered plot from raw data, find the smallest and largest values and the mode, notice clusters, gaps and outliers, and compare two groups with a back-to-back plot. Comparing two classes’ test marks or two swimming clubs’ times is a typical use. This subtopic is part of Year 7 Analysing Data.
Theory
A stem-and-leaf plot splits each value into a stem and a leaf, so it shows every data value in order, grouped by tens. The key tells you how to read it: Key: 3 | 7 \(= 37\). This Year 7 maths page shows how to draw, read and compare stem-and-leaf plots.
Parts. Usually the stem is the tens digit and the leaf is the ones digit, but always check the key. Each leaf is one data value.
Drawing. Sort the data from smallest to largest. Write the stems down the left, then put each value’s ones digit on its stem, smallest to largest (an ordered plot). Keep repeated leaves, and check that the number of leaves matches the number of values.
Reading. The smallest value is the first leaf on the first stem. The largest value is the last leaf on the last stem. The number of values is the number of leaves. The mode is the value whose leaf repeats most in one row (read it with its stem). Median: count the leaves, find the middle position \(\dfrac{n + 1}{2}\) and count along the ordered leaves. Mean: add every value (stem and leaf together) and divide by the number of leaves.
Features. Keep a stem with no leaves: it shows a gap. Look for clusters (rows with many leaves) and outliers (values far from the rest).
Back-to-back plots compare two groups. The stems are in the middle. The leaves on the left are read from the stem outwards, so the leaf next to the stem is the smallest.
Always read the key first:
| Key | Stem | Leaf |
|---|---|---|
| 3 | 7 = 37 | tens | ones |
| 0 | 6 = 6 | 0 tens | ones |
| 15 | 3 = 153 cm | first two digits | ones |
| 3 | 2 = 3.2 kg | ones | tenths |
How to draw a stem-and-leaf plot
- Order the data from smallest to largest.
- Write the stems in a column (include any empty stems).
- Add each leaf to its stem, in order, keeping repeats.
- Write a key and check the number of leaves.
(i) What is the best score?
(ii) How many students did the test?
(iii) What is the range?
(iv) What is the mode?
(v) What is the median?
| Stem | Leaf |
|---|---|
| 5 | 1 4 7 |
| 6 | 3 3 5 6 |
| 7 | 7 8 8 8 9 9 |
| 8 | 5 6 6 8 |
| 9 | 1 2 2 |
Key: 7 | 8 = 78
| \(3 + 4 + 6 + 4 + 3\) | \(=\) | \(20\) |
| \(92 - 51\) | \(=\) | \(41\) |
(i) \(92\) (last leaf on the last stem)
(ii) \(20\) students (count the leaves)
(iii) \(41\)
(iv) \(78\): the leaf \(8\) appears three times on stem \(7\).
(v) \(20\) leaves, so the median is halfway between the \(10\)th and \(11\)th values. Counting along, both are \(78\): median \(78\).
(i) What is the most laps swum?
(ii) How many swimmers are there?
(iii) What is the mode?
| Stem | Leaf |
|---|---|
| 1 | 4 7 9 |
| 2 | 0 3 3 3 6 8 |
| 3 | 1 5 5 |
| 4 | 2 |
Key: 2 | 3 = 23 laps
| \(3 + 6 + 3 + 1\) | \(=\) | \(13\) |
(i) \(42\) laps
(ii) \(13\)
(iii) \(23\) laps (three times)
Sort first: \(29, 35, 35, 38, 40, 42, 44, 47, 51, 53\). Then split each score into a stem (tens) and a leaf (ones).
| Stem | Leaf |
|---|---|
| 2 | 9 |
| 3 | 5 5 8 |
| 4 | 0 2 4 7 |
| 5 | 1 3 |
Key: 4 | 2 = 42 points
| \(1 + 3 + 4 + 2\) | \(=\) | \(10\) |
Check: \(10\) leaves. Both \(35\)s stay, as 3 | 5 5.
(i) What was the longest jump?
(ii) How many jumped less than \(3.5\) m?
(iii) Which distance is an outlier?
| Stem | Leaf |
|---|---|
| 1 | 5 |
| 2 | |
| 3 | 1 3 4 6 6 8 9 |
| 4 | 0 2 2 2 5 |
Key: 3 | 4 = 3.4 m
The stem is whole metres and the leaf is tenths.
(i) \(4.5\) m
(ii) \(4\) (\(1.5, 3.1, 3.3, 3.4\))
(iii) \(1.5\) m: stem \(2\) is empty (a gap), so it is far below the rest.
(i) What is the lowest mark in 7R?
(ii) How many in each class scored \(30\) or more?
(iii) Which class did better?
| 7R | Stem | 7S |
|---|---|---|
| 9 5 | 1 | |
| 8 6 4 1 | 2 | 7 |
| 7 3 0 | 3 | 2 5 6 8 |
| 2 | 4 | 0 1 3 4 7 |
Key: 1 | 2 | 7 means 21 for 7R and 27 for 7S
| \(3 + 1\) | \(=\) | \(4\) |
| \(4 + 5\) | \(=\) | \(9\) |
(i) \(15\) (the leaf next to the stem)
(ii) 7R: \(4\), 7S: \(9\)
(iii) 7S: most of its marks are in the \(30\)s and \(40\)s.
Common pitfalls
Frequently asked questions
What is a stem-and-leaf plot?
A table that splits each value into a stem (usually tens) and a leaf (usually ones), showing every value in order.
How do you count the values in a stem-and-leaf plot?
Count the leaves.
How do you find the mode?
Look for the leaf that repeats most in one row, and read it with its stem.
Why do you need a key?
It shows the place value: 3 | 4 could be \(34\) or \(3.4\).
How do you read the left side of a back-to-back plot?
From the stem outwards: the leaf next to the stem is the smallest.