Organising data & statistical charts · Ages 12–13
What the diagrams tell us
A histogram doesn't show the values inside a class.
How to do it
Method
A histogram doesn't show the values inside a class
5 in 60–69, 3 in 70–79: at least 3 scored 65 or more, at most 8
Another way
Find a counter-example
The 5 might all score 60: so only 'at least 3'
In full
Before concluding anything, ask what the picture can tell you. A stem-and-leaf diagram keeps every value, so the greatest, the least, and how many lie above a value are all known exactly. A histogram tells only how many are in each class, not their exact values: if the class 60–69 holds 5 people, the number scoring 65 or more can't be pinned down; there are at least those in 70 and above, and at most those plus the 5. To judge a statement: work its quantity out from the picture and compare; or look for a counter-example, one case that breaks it, and then it isn't certain. A percentage = part ÷ total × 100%; 'twice as many' is 2 times.
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 highest score is 41
- B. 8 players scored 30 or more
- C. The team has 10 players
- D. The lowest score is 25
Choose the right answer
Show the answer and working
Answer: D. The lowest score is 25
Read off the diagram: highest 39, lowest 25, 11 players, 7 scoring 30 or more; then check each statement.
Example 2
The histogram shows a team's scores. At most how many players scored 55 or more?
Show the answer and working
Answer: 10
Everyone in 50–59 might be 55 or more, so add that class and every one after: at most 10.
Example 3
The stem-and-leaf diagram shows 20 players' scores. What percentage of them scored 50 or more?
Show the answer and working
Answer: 40%
8 scored 50 or more: 8 ÷ 20 × 100% = 40%.
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 60 or more.
True or false?
Answer:
2.The histogram shows a team's scores. Which statement is right?
- A. 12 players scored 60–69
- B. 17 players scored under 50
- C. The team has 41 players
- D. 24 players scored 50 or more
Choose the right answer
Answer:
3.The stem-and-leaf diagram shows 20 players' scores. What percentage of them scored 50 or more?
Answer:
4.The histogram shows a team's scores. At most how many players scored 56 or more?
Answer:
5.Ming draws the team's scores as a histogram, one class being 40–49. From the histogram alone, which of these can be found?
- A. How many scored 40–49
- B. The highest score in 40–49
- C. How many scored 47 or more
- D. How many scored exactly 47
Choose the right answer
Answer:
All the answers
- 1. False
- 2. D. 24 players scored 50 or more
- 3. 35%
- 4. 24
- 5. A. How many scored 40–49
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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