Organising data & statistical charts · Ages 12–13
Drawing stem-and-leaf diagrams
Keep empty stems; each row's leaves in order.
How to do it
Method
Keep empty stems; each row's leaves in order
Data 41, 43, 62: stems 4, 5, 6, stem 5's row empty
Another way
Sort the data first
41, 43, 62 → 4 | 1 3, 6 | 2
In full
To draw a stem-and-leaf diagram: find the least and greatest values, write every stem from smallest to largest, including a stem with no data (its row left empty); write each value's leaf beside its stem, then put each row's leaves in order and add a key (such as 4 | 5 = 45). A three-digit value, a height of 152 cm say, can take its first two digits, 15, as the stem and the units, 2, as the leaf. Or sort the data first and write the leaves in turn, with nothing to reorder. Check: there are as many leaves as values, and the number of stems = the largest stem − the smallest + 1, not the number of stems that have data.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
These 10 values go in a stem-and-leaf diagram, the tens digit as the stem: 54, 21, 43, 33, 47, 22, 54, 47, 47, 23. Which stem's row has the most leaves?
Show the answer and working
Answer: 4
Count the values with each tens digit: tens digit 4 has the most, 4, so stem 4's row has the most leaves.
Example 2
These 8 values go in a stem-and-leaf diagram, the tens digit as the stem: 56, 30, 38, 58, 35, 28, 59, 31. Stem 2's row has 1 leaves.
True or false?
Show the answer and working
Answer: True
Count the values with tens digit 2: 1, so stem 2's row has 1 leaves.
Example 3
The stem-and-leaf diagram (the tens digit as the stem) should show these 8 values, but one is missing: 27, 40, 35, 39, 23, 42, 31, 25. Which value is missing?
Show the answer and working
Answer: 39
First check the number of leaves: the diagram has only 7, but there are 8 values. Find each value in the diagram in turn; the one not there is 39.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A stem-and-leaf diagram of these data, the tens digit as the stem: 61, 48, 15, 60, 75, 42. Counting from the smallest stem to the largest, how many stems are written?
Answer:
2.Here are 8 values: 32, 38, 48, 35, 25, 32, 52, 24. Which stem-and-leaf diagram shows them correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
3.These 8 values go in a stem-and-leaf diagram, the tens digit as the stem: 31, 56, 33, 40, 46, 28, 24, 29. Stem 5's row has 1 leaves.
True or false?
Answer:
4.These 10 values go in a stem-and-leaf diagram, the tens digit as the stem: 26, 43, 46, 62, 61, 59, 33, 59, 64, 62. Which stem's row has the most leaves?
Answer:
5.The stem-and-leaf diagram (the tens digit as the stem) should show these 8 values, but one is missing: 57, 28, 30, 20, 28, 23, 50, 30. Which value is missing?
Answer:
All the answers
- 1. 7
- 2. A
- 3. True
- 4. 6
- 5. 23
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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