Organising data & statistical charts · Ages 12–13
Back-to-back stem-and-leaf diagrams
The left side too reads stem, then leaf.
How to do it
Method
The left side too reads stem, then leaf
On the left, 3 | 6 is 63, not 36
Another way
Write two lists
A: 52, 58, 63; B: 49, 61, 70
In full
A back-to-back stem-and-leaf diagram puts two sets of data on the two sides of one stem, to compare them. The right side reads as usual: stem 6, leaf 3 is 63. The left side's leaves run outwards from the stem, the smallest nearest it, and still read stem first, then leaf: leaf 3 beside stem 6 on the left is 63 as well, not 36. To compare the sets, count how many in each lie above a value, compare the greatest and least, or see which side's leaves gather on the larger stems. Or write each side's values out in two lists and compare those.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). What is team B's highest score?
Show the answer and working
Answer: 51
Team B is on the right: the last row's outermost leaf, read stem then leaf: 51.
Example 2
The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). Which team has more players scoring 70 or more?
- A. Team B
- B. Team A
- C. Can't be told
- D. The same in both
Choose the right answer
Show the answer and working
Answer: A. Team B
Count the leaves from stem 7 on: team A (left) 2, team B (right) 4.
Example 3
The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). By how much do the two teams' highest scores differ?
Show the answer and working
Answer: 4
Team A's highest is 59, team B's 55: a difference of 4.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). What is team B's highest score?
Answer:
2.The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). What is team A's lowest score?
Answer:
3.The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). How many in team A scored 62 or more?
Answer:
4.The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). Scoring 60 or more: team A , team B .
Fill in each blank
Answer:
5.The back-to-back stem-and-leaf diagram shows 10 scores each from team A (left) and team B (right). What is team A's lowest score?
- A. 51
- B. 15
- C. 42
- D. 73
Choose the right answer
Answer:
All the answers
- 1. 47
- 2. 44
- 3. 1
- 4. 2, 0
- 5. A. 51
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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