Data and probability · Ages 13–14

Histograms worksheet

Part of: Cumulative frequency & charts

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Data and probability · Ages 13–14

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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. How many players are in the team?
Answer:
2.The histogram shows a team's scores. How many scored 60–69?
Answer:
3.The table is drawn as a histogram (the left column is scores, the right players). The bar for 60–69 runs along the axis from to , and is tall.
Fill in each blank
Answer:
4.The histogram shows a team's scores. How many scored 60 or more?
Answer:
5.These 10 values are grouped and drawn as a histogram: 57, 31, 66, 48, 54, 36, 36, 39, 69, 29. How tall is the bar for 50–59?
Answer:
6.The histogram shows a team's scores. At least how many players scored 51 or more?
Answer:
7.The histogram shows the scores of a team of 25. What percentage of them scored 60 or more?
Answer:

8.The histogram shows a team's heights in cm. Which class has the most players?
- A. 150–154
- B. 140–144
- C. 145–149
- D. 155–159
Choose the right answer
Answer:
9.Data grouped as 70–79, 80–89, … are drawn as a histogram. At which two values on the horizontal axis are the first bar's edges?
- A. 74.5、84.5
- B. 69.5、79.5
- C. 70、89
- D. 70、79
Choose the right answer
Answer:
10.The histogram shows a team's scores. From it we can be sure that at least 13 players scored 67 or more.
True or false?
Answer:
11.Tsz-ching draws the team's scores as a histogram, one class being 50–59. From the histogram alone, which of these can be found?
- A. How many scored exactly 57
- B. How many scored 50–59
- C. How many scored 57 or more
- D. The highest score in 50–59
Choose the right answer
Answer:
12.The histogram shows a team's scores, its axis marked with class boundaries. More players scored below 79.5 than above it.
True or false?
Answer:

13.Tsz-ching groups these 10 values as 20–29, 30–39, 40–49, 50–59 and draws a histogram: 30, 38, 37, 51, 22, 28, 33, 39, 57, 36. How tall is the tallest bar?
Working:
Answer:
14.The histogram shows a team's scores. The class 40–49 has more players than 60–69; together they have .
Fill in each blank
Working:
Answer:
15.The histogram shows a team's scores, its axis marked with class marks; the width is 10. How many players are in the classes with mark 84.5 or more?
Working:
Answer:
16.The histogram shows the scores in Chi-keung's team; the target score is 36. From the histogram alone, at least how many reached it?
Working:
Answer:
17.The histogram shows the scores in Ming's team; the target score is 65. From the histogram alone, at most how many fell short of it?
Working:
Answer:
18.Ming's team has 35 players. The histogram shows their heights in cm, but the bar for 150–154 is missing. How many are in that class?
Working:
Answer:

Show the answers and working

Histograms worksheet: Answers and working

1. 23
The five bars' heights from 30 on, added: 6 + 6 + 1 + 4 + 6 = 23.
2. 11
Read across from the top of the 60–69 bar to the scale: 11.
3. 59.5, 69.5, 10
The bar runs from the lower boundary 59.5 to the upper 69.5, as tall as the frequency 10.
4. 20
From the class starting at 60, add the heights of it and every bar after: 20.
5. 2
A bar's height is its class's frequency: count the values from 50 to 59, 2 of them.
6. 23
Everyone in 50–59 might be under 51, so only the classes from 60 on are certain: 23 players.
7. 44%
60 or more: 11 players; 11 ÷ 25 × 100% = 44%.

8. D. 155–159
The tallest bar stands for 14 players: see which class it is.
9. B. 69.5、79.5
The class 70–79 has boundaries 69.5 and 79.5: the bar runs from one to the other and touches the next.
10. True
Only the 15 scoring 70 or more are certain (the class holding 67 might all be under it). We can be sure only if 13 is no more than 15.
11. B. How many scored 50–59
A histogram shows each class's frequency: the 50–59 bar's height is its number; the scores inside it don't show.
12. True
The bars left of 79.5 hold 20; those right of it 18.

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

13. 6
The classes' frequencies are 2, 6, 0, 2; the tallest bar is the greatest, 6.
14. 4, 20
40–49 has 12, 60–69 has 8: 12 − 8 = 4, 12 + 8 = 20.
15. 6
From the bar at mark 84.5, add its height and every bar's to the right: 6.
16. 22
Everyone in 30–39 might be under 36, so only those in the classes from 40 on surely reached it: 22.
17. 26
Everyone in 60–69 might be under 65, so add that class and those before it: at most 26 fell short.
18. 5
The other bars hold 30: 35 − 30 = 5.

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