Organising data & statistical charts · Ages 12–13
Interpreting stem-and-leaf diagrams
One leaf, one value: count, then compare.
How to do it
Method
One leaf, one value: count, then compare
13 of 20 pass: 13 ÷ 20 × 100% = 65%
Another way
Find a counter-example
'All over 40': one 38 makes it wrong
In full
Before concluding anything, ask what the picture can tell you. A stem-and-leaf diagram keeps every value, its leaves already in order, so the greatest, the least, the 3rd highest, and how many lie above or below a value can all be counted exactly. To judge a statement: work its quantity out from the diagram and compare — for 'over half passed', compare those who passed with half the team; or look for a counter-example, one value that breaks it, and then it is wrong. A percentage = part ÷ whole × 100%. Adding a value changes the whole too: 3 passes in 4 (75%), joined by one who fails, become 3 in 5 (60%).
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The stem-and-leaf diagram shows a team's scores. Which statement is right?
- A. The team has 12 players
- B. 9 players scored 40 or more
- C. The lowest score is 36
- D. The highest score is 55
Choose the right answer
Show the answer and working
Answer: A. The team has 12 players
Read off the diagram: highest 56, lowest 35, 12 players, 8 scoring 40 or more; then check each statement.
Example 2
The stem-and-leaf diagram shows a team's scores; 40 or more is a pass. How many did not pass?
Show the answer and working
Answer: 6
Not passing is under 40: count the leaves in the rows before 40's, 6. Or take those who passed from the team of 14.
Example 3
The stem-and-leaf diagram shows 20 players' scores; 60 or more gets a place. get a place; those who don't are % of the team.
Fill in each blank
Show the answer and working
Answer: 4, 80
4 scored 60 or more; 20 − 4 did not, (20 − 4) ÷ 20 × 100% = 80%.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The stem-and-leaf diagram shows a team's scores. At least one player scored 67 or more.
True or false?
Answer:
2.The stem-and-leaf diagram shows a team's scores. Which statement is right?
- A. The highest score is 58
- B. The team has 14 players
- C. 11 players scored 40 or more
- D. The lowest score is 37
Choose the right answer
Answer:
3.The stem-and-leaf diagram shows a team's scores; 40 or more is a pass. How many did not pass?
Answer:
4.The stem-and-leaf diagram shows a team's scores. More players scored 40 or more than scored under 40.
True or false?
Answer:
5.The stem-and-leaf diagram shows 20 players' scores; 60 or more gets a place. get a place; those who don't are % of the team.
Fill in each blank
Answer:
All the answers
- 1. False
- 2. B. The team has 14 players
- 3. 2
- 4. True
- 5. 4, 80
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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