Organising data & statistical charts · Ages 12–13
Class limits, boundaries and marks
A boundary is halfway between classes; mark = (lower + upper limit) ÷ 2.
How to do it
Method
A boundary is halfway between classes; mark = (lower + upper limit) ÷ 2
40–49: boundaries 39.5 and 49.5, mark 44.5, width 10
Another way
From the boundaries
(39.5 + 49.5) ÷ 2 = 44.5; 49.5 − 39.5 = 10
In full
When there are many spread-out data, put them in classes. In the class 40–49, 40 is the lower class limit and 49 the upper: the least and greatest values in it. A class boundary lies halfway between two classes: between 49 and 50 is 49.5, so 40–49 has lower boundary 39.5 and upper boundary 49.5. The class mark is the middle of the class: (lower limit + upper limit) ÷ 2 = (40 + 49) ÷ 2 = 44.5, the same as (39.5 + 49.5) ÷ 2. The class width is its breadth: upper boundary − lower boundary = 49.5 − 39.5 = 10; or take one class's lower limit from the next one's: 50 − 40 = 10. Careful: the width is not 49 − 40 = 9, and the mark is not (40 + 50) ÷ 2 = 45.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The class mark of the class 80–99 is .
Show the answer and working
Answer: 89.5
Class mark = (lower limit + upper limit) ÷ 2 = (80 + 99) ÷ 2 = 89.5.
Example 2
The class 90–99 has lower class limit and upper class limit .
Fill in each blank
Show the answer and working
Answer: 90, 99
The class limits are the least and greatest values in it: lower 90, upper 99.
Example 3
The class mark of the class 20–29 is 24.5.
True or false?
Show the answer and working
Answer: True
Class mark = (20 + 29) ÷ 2 = 24.5, not (20 + 30) ÷ 2.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The class mark of the class 45–49 is .
Answer:
2.The class 120–139 has lower class boundary and upper class boundary .
Fill in each blank
Answer:
3.The class mark of the class 40–59 is 49.5.
True or false?
Answer:
4.Three classes in a row have class marks 169.5, 189.5, 209.5. The second class is –.
Fill in each blank
Answer:
5.A class has lower boundary 49.5 and width 5. Its class mark is .
Answer:
All the answers
- 1. 47
- 2. 119.5, 139.5
- 3. True
- 4. 180, 199
- 5. 52
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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