Data and probability · Ages 12–13

Class limits, boundaries and marks worksheet

Part of: Organising data & statistical charts

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Data and probability · Ages 12–13

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

1.The class 40–49 has lower class boundary and upper class boundary .
Fill in each blank
Answer:
2.The class 30–39 has lower class limit and upper class limit .
Fill in each blank
Answer:
3.The class mark of the class 30–34 is .
Answer:
4.The class 30–34 has lower class limit and upper class limit .
Fill in each blank
Answer:
5.The class 30–34 has lower class boundary and upper class boundary .
Fill in each blank
Answer:
6.The data are grouped as 100–119, 120–139, 140–159. The class width is .
Answer:
7.The data are grouped as 20–23, 24–27, 28–31. The class width is .
Answer:
8.Three classes in a row have class marks 37, 42, 47. The second class is –.
Fill in each blank
Answer:
9.A class has lower boundary 259.5 and width 20. Its class mark is .
Answer:

13.Ming groups teammates' heights as 150–159, 160–169, 170–179 cm. The second class's lower boundary is cm, its upper boundary cm, and its class mark cm.
Fill in each blank
Working:
Answer:
14.Ka-yan groups the team's scores as 30–39, 40–… and so on. What is the class mark of 30–39?
- A. 35
- B. 34.5
- C. 29.5
- D. 39.5
Choose the right answer
Working:
Answer:
15.The histogram shows how many minutes a week Chi-keung's teammates exercise. What is the class mark of the class with the most players?
Working:
Answer:
16.Teammates' heights are measured to the nearest cm and grouped as 140–149, 150–159, 160–169, 170–179 cm. Ka-yan is really 169.6 cm tall. Which class does Ka-yan go in?
- A. 150–159
- B. 140–149
- C. 160–169
- D. 170–179
Choose the right answer
Working:
Answer:
17.Chi-keung says, 'The boundary between the classes 45–49 and 50–54 is 50.' Chi-keung is right.
True or false?
Working:
Answer:
18.In Ka-yee's histogram, one bar runs from 99.5 to 119.5. That bar is the class –, with class mark .
Fill in each blank
Working:
Answer:

Show the answers and working

Class limits, boundaries and marks worksheet: Answers and working

1. 39.5, 49.5
A boundary is halfway between classes: between the class below's upper limit 39 and 40 is 39.5; between 49 and the next class's lower limit 50 is 49.5.
2. 30, 39
The class limits are the least and greatest values in it: lower 30, upper 39.
3. 32
Class mark = (lower limit + upper limit) ÷ 2 = (30 + 34) ÷ 2 = 32.
4. 30, 34
The class limits are the least and greatest values in it: lower 30, upper 34.
5. 29.5, 34.5
A boundary is halfway between classes: between the class below's upper limit 29 and 30 is 29.5; between 34 and the next class's lower limit 35 is 34.5.
6. 20
Take one class's lower limit from the next one's: 120 − 100 = 20. Careful: 119 − 100 = 19 is not the width, as 100 to 119 takes in 20 whole numbers.
7. 4
Take one class's lower limit from the next one's: 24 − 20 = 4. Careful: 23 − 20 = 3 is not the width, as 20 to 23 takes in 4 whole numbers.
8. 40, 44
Width = 42 − 37 = 5. The second class's boundaries are 42 − 2.5 = 39.5 and 42 + 2.5 = 44.5, so the class is 40–44.
9. 269.5
The mark is halfway between the boundaries: 259.5 + 20 ÷ 2 = 259.5 + 10 = 269.5. Or the class is 260–279: (260 + 279) ÷ 2 = 269.5.

10. A. 49.5
The boundary is halfway between 49 and the next class's lower limit 50: (49 + 50) ÷ 2 = 49.5.
11. True
Class mark = (20 + 29) ÷ 2 = 24.5, not (20 + 30) ÷ 2.
12. True
Class mark = (40 + 44) ÷ 2 = 42, not (40 + 45) ÷ 2.

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

13. 159.5, 169.5, 164.5
The second class is 160–169: its boundaries lie halfway to its neighbours, 159.5 and 169.5; its mark = (160 + 169) ÷ 2 = 164.5.
14. B. 34.5
Mark = (lower limit + upper limit) ÷ 2 = (30 + 39) ÷ 2.
15. 74.5
The tallest bar is 70–79 (9 players). Its mark = (70 + 79) ÷ 2 = 74.5.
16. D. 170–179
Round first: 169.6 cm is recorded as 170 cm; then find its class. Or use the boundaries 149.5, 159.5, 169.5: see which two 169.6 lies between.
17. False
The boundary is halfway between 49 and 50: (49 + 50) ÷ 2 = 49.5.
18. 100, 119, 109.5
99.5 and 119.5 are boundaries; the whole numbers between run from 100 to 119; the mark is halfway: (99.5 + 119.5) ÷ 2 = 109.5.

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