Data and probability · Ages 12–13

What the diagrams tell us worksheet

Part of: Organising data & statistical charts

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Data and probability · Ages 12–13

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The histogram shows a team's scores. At least how many players scored 85 or more?
Answer:
2.The histogram shows a team's scores. At least how many players scored 63 or more?
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 81 or more?
Answer:
5.The histogram shows a team's scores. At most how many players scored 56 or more?
Answer:

6.The stem-and-leaf diagram shows a team's scores. Which statement is right?
- A. The highest score is 61
- B. 12 players scored 40 or more
- C. The team has 15 players
- D. The lowest score is 41
Choose the right answer
Answer:
7.The stem-and-leaf diagram shows a team's scores. At least one player scored 62 or more.
True or false?
Answer:
8.The stem-and-leaf diagram shows a team's scores. At least one player scored 48 or more.
True or false?
Answer:
9.The histogram shows a team's scores. Which statement is right?
- A. 25 players scored 50 or more
- B. 20 players scored under 50
- C. 8 players scored 40–49
- D. The team has 47 players
Choose the right answer
Answer:
10.The histogram shows a team's scores. From it we can be sure that at least 6 players scored 78 or more.
True or false?
Answer:
11.Chi-keung draws the team's scores as a histogram, one class being 30–39. From the histogram alone, which of these can be found?
- A. How many scored exactly 38
- B. How many scored 38 or more
- C. The highest score in 30–39
- D. How many scored 30–39
Choose the right answer
Answer:
12.May draws the team's scores as a histogram, one class being 60–69. From the histogram alone, which of these can be found?
- A. How many scored 60–69
- B. How many scored 68 or more
- C. The highest score in 60–69
- D. How many scored exactly 68
Choose the right answer
Answer:

13.The histogram shows the scores in May's team; the target score is 46. From the histogram alone, at least how many reached it?
Working:
Answer:
14.The stem-and-leaf diagram shows the scores in Tsz-hin's team. Which statement is right?
- A. The 2nd lowest score is 26
- B. 10 players scored 30 or more
- C. 3 players scored under 30
- D. The highest and lowest differ by 21
Choose the right answer
Working:
Answer:
15.The histogram shows a team's scores. Chi-keung says, 'From the histogram, exactly 19 players scored 53 or more, for certain.' Chi-keung is right.
True or false?
Working:
Answer:
16.The histogram shows the scores in Tsz-ching's team; the target score is 56. From the histogram alone, at most how many fell short of it?
Working:
Answer:
17.The histogram shows 25 players' scores. scored 70 or more, which is % of them.
Fill in each blank
Working:
Answer:
18.The stem-and-leaf diagram shows 20 players' scores. More than 40% of them scored 50 or more.
True or false?
Working:
Answer:

Show the answers and working

What the diagrams tell us worksheet: Answers and working

1. 11
Everyone in 80–89 might be under 85, so only the classes from 90 on are certain: 11 players.
2. 10
Everyone in 60–69 might be under 63, so only the classes from 70 on are certain: 10 players.
3. 50%
10 scored 50 or more: 10 ÷ 20 × 100% = 50%.
4. 16
Everyone in 80–89 might be 81 or more, so add that class and every one after: at most 16.
5. 25
Everyone in 50–59 might be 56 or more, so add that class and every one after: at most 25.

6. A. The highest score is 61
Read off the diagram: highest 61, lowest 38, 14 players, 10 scoring 40 or more; then check each statement.
7. True
The highest score is 63. Someone scored 62 or more only if 62 is no more than 63.
8. True
The highest score is 51. Someone scored 48 or more only if 48 is no more than 51.
9. A. 25 players scored 50 or more
Read off the histogram: 46 in all; 10 in 40–49; 25 scoring 50 or more; 21 under 50.
10. False
Only the 4 scoring 80 or more are certain (the class holding 78 might all be under it). We can be sure only if 6 is no more than 4.
11. D. How many scored 30–39
A histogram shows each class's frequency: the 30–39 bar's height is its number; the scores inside it don't show.
12. A. How many scored 60–69
A histogram shows each class's frequency: the 60–69 bar's height is its number; the scores inside it don't show.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 11
Everyone in 40–49 might be under 46, so only those in the classes from 50 on surely reached it: 11.
14. A. The 2nd lowest score is 26
Read off the diagram: 2 under 30, 9 at 30 or more, a gap of 20 between highest and lowest, 26 2nd lowest; then check each.
15. False
Only when 53 is a team's lower limit can the number be certain (then it is the classes from 53 on); with 53 inside a class, how many of that class are above it doesn't show.
16. 38
Everyone in 50–59 might be under 56, so add that class and those before it: at most 38 fell short.
17. 4, 16
70 or more: the bars from 70 on, 4; 4 ÷ 25 × 100% = 16%.
18. True
15 scored 50 or more: 15 ÷ 20 × 100% = 75%. Compare 75% with 40%.

Numsprite · numsprite.com/en/worksheets/organising-data-and-statistical-charts/interpreting-stem-and-leaf-diagrams-and-histograms