The class 40–49 has lower class limit □ and upper class limit □. Fill in each blank

40, 49. The class limits are the least and greatest values in it: lower 40, upper 49.

The class 20–29 has lower class boundary □ and upper class boundary □. Fill in each blank

19.5, 29.5. A boundary is halfway between classes: between the class below's upper limit 19 and 20 is 19.5; between 29 and the next class's lower limit 30 is 29.5.

What is the upper class boundary of the class 25–29? A. 30 B. 29 C. 28.5 D. 29.5 Choose the right answer

D. 29.5. The boundary is halfway between 29 and the next class's lower limit 30: (29 + 30) ÷ 2 = 29.5.

Cumulative frequency & charts · Ages 13–14

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 class boundary 39.5 and upper class 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 class boundary − lower class 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 40–49 has lower class limit and upper class limit .
Fill in each blank
Show the answer and working
Answer: 40, 49
The class limits are the least and greatest values in it: lower 40, upper 49.
Example 2
The class 20–29 has lower class boundary and upper class boundary .
Fill in each blank
Show the answer and working
Answer: 19.5, 29.5
A boundary is halfway between classes: between the class below's upper limit 19 and 20 is 19.5; between 29 and the next class's lower limit 30 is 29.5.
Example 3
What is the upper class boundary of the class 25–29?
- A. 30
- B. 29
- C. 28.5
- D. 29.5
Choose the right answer
Show the answer and working
Answer: D. 29.5
The boundary is halfway between 29 and the next class's lower limit 30: (29 + 30) ÷ 2 = 29.5.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.The class 70–79 has lower class limit and upper class limit .
Fill in each blank
Answer:
2.The class mark of the class 40–49 is .
Answer:
3.The data are grouped as 10–19, 20–29, 30–39. The class width is .
Answer:
4.What is the upper class boundary of the class 140–159?
- A. 159
- B. 159.5
- C. 160
- D. 158.5
Choose the right answer
Answer:
5.Three classes in a row have class marks 64.5, 74.5, 84.5. The second class is –.
Fill in each blank
Answer:

All the answers

1. 70, 79
2. 44.5
3. 10
4. B. 159.5
5. 70, 79

Free worksheet: Class limits, boundaries and marksWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

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

Start playingPlay and learn in the secondary world, Star Galaxy: animated methods, monster battles, a review of every mistake