Data and probability · Ages 13–14

Class limits, boundaries and marks worksheet

Part of: Cumulative frequency & charts

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Data and probability · Ages 13–14

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

1.The class 80–99 has lower class boundary and upper class boundary .
Fill in each blank
Answer:
2.The class 80–89 has lower class limit and upper class limit .
Fill in each blank
Answer:
3.The class mark of the class 40–44 is .
Answer:
4.The class 25–29 has lower class boundary and upper class boundary .
Fill in each blank
Answer:
5.The class 30–34 has lower class limit and upper class limit .
Fill in each blank
Answer:
6.The data are grouped as 20–24, 25–29, 30–34. The class width is .
Answer:
7.A class has lower boundary 27.5 and width 4. Its class mark is .
Answer:
8.Three classes in a row have class marks 44.5, 54.5, 64.5. The second class is –.
Fill in each blank
Answer:

13.Ka-yan records each day's highest temperature for a month (°C, to the nearest whole number), grouped as 18–20, 21–23, 24–26. What is the class width in °C?
Working:
Answer:
14.Tsz-hin says, 'The boundary between the classes 40–49 and 50–59 is 49.5.' Tsz-hin is right.
True or false?
Working:
Answer:
15.In May's histogram, one bar runs from 299.5 to 319.5. That bar is the class –, with class mark .
Fill in each blank
Working:
Answer:
16.Chi-keung groups teammates' heights as 140–144, 145–149, 150–154 cm. The second class's lower boundary is cm, its upper boundary cm, and its class mark cm.
Fill in each blank
Working:
Answer:
17.Players' weights are measured to the nearest 0.1 kg, and one class is 33.0–37.9 kg. Its lower boundary is kg, its upper boundary kg, and its class mark kg.
Fill in each blank
Working:
Answer:
18.Teammates' heights are measured to the nearest cm and grouped as 140–149, 150–159, 160–169, 170–179 cm. Chi-keung is really 149.6 cm tall. Which class does Chi-keung go in?
- A. 140–149
- B. 170–179
- C. 160–169
- D. 150–159
Choose the right answer
Working:
Answer:

Show the answers and working

Class limits, boundaries and marks worksheet: Answers and working

1. 79.5, 99.5
A boundary is halfway between classes: between the class below's upper limit 79 and 80 is 79.5; between 99 and the next class's lower limit 100 is 99.5.
2. 80, 89
The class limits are the least and greatest values in it: lower 80, upper 89.
3. 42
Class mark = (lower limit + upper limit) ÷ 2 = (40 + 44) ÷ 2 = 42.
4. 24.5, 29.5
A boundary is halfway between classes: between the class below's upper limit 24 and 25 is 24.5; between 29 and the next class's lower limit 30 is 29.5.
5. 30, 34
The class limits are the least and greatest values in it: lower 30, upper 34.
6. 5
Take one class's lower limit from the next one's: 25 − 20 = 5. Careful: 24 − 20 = 4 is not the width, as 20 to 24 takes in 5 whole numbers.
7. 29.5
The mark is halfway between the boundaries: 27.5 + 4 ÷ 2 = 27.5 + 2 = 29.5. Or the class is 28–31: (28 + 31) ÷ 2 = 29.5.
8. 50, 59
Width = 54.5 − 44.5 = 10. The second class's boundaries are 54.5 − 5 = 49.5 and 54.5 + 5 = 59.5, so the class is 50–59.

9. B. 24.5
The boundary is halfway between 24 and the next class's lower limit 25: (24 + 25) ÷ 2 = 24.5.
10. False
Class mark = (180 + 199) ÷ 2 = 189.5, not (180 + 200) ÷ 2.
11. False
Class mark = (100 + 119) ÷ 2 = 109.5, not (100 + 120) ÷ 2.
12. C. 139.5
The boundary is halfway between 139 and the next class's lower limit 140: (139 + 140) ÷ 2 = 139.5.

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

13. 3°C
Width = upper boundary − lower boundary, the same as the gap between two lower limits: 21 − 18 = 3. Not 20 − 18 = 2.
14. True
The boundary is halfway between 49 and 50: (49 + 50) ÷ 2 = 49.5.
15. 300, 319, 309.5
299.5 and 319.5 are boundaries; the whole numbers between run from 300 to 319; the mark is halfway: (299.5 + 319.5) ÷ 2 = 309.5.
16. 144.5, 149.5, 147
The second class is 145–149: its boundaries lie halfway to its neighbours, 144.5 and 149.5; its mark = (145 + 149) ÷ 2 = 147.
17. 32.95, 37.95, 35.45
With data to 0.1, a boundary lies halfway between neighbouring values: just below 33.0 is 32.95; between 37.9 and the next class's start, 37.9 + 0.1, is 37.95. Mark = (33 + 37.9) ÷ 2 = 35.45.
18. D. 150–159
Round first: 149.6 cm is recorded as 150 cm; then find its class. Or use the boundaries 149.5, 159.5, 169.5: see which two 149.6 lies between.

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