Cumulative frequency & charts · Ages 14–15
Frequency polygons
Points at the class marks; a 0 class at each end.
How to do it
Method
Points at the class marks; a 0 class at each end
40–49: class mark (40 + 49) ÷ 2 = 44.5
Another way
Join the bars' tops
Draw the histogram, then join the middles of the bars' tops
In full
A frequency polygon plots each class's frequency at its class mark and joins the points in order with straight lines; the class mark = (lower limit + upper limit) ÷ 2, so 40–49 has class mark (40 + 49) ÷ 2 = 44.5. At each end it adds a class with frequency 0 (one before the first class, one after the last), so the polygon comes back down to the axis. One way to draw it: take each class mark and frequency straight from the frequency table and plot them. Another: draw the histogram first and join the middles of the bars' tops: the same polygon. Reading it, each point's height is its class's frequency, and the heights add up to the total frequency (the 0s at the ends change nothing).
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The frequency polygon shows the ages (in years) of a gym's members. How many are in the class with class mark 62?
Show the answer and working
Answer: 8 people
Go up from 62 on the axis: the point's height is the frequency, 8.
Example 2
The frequency polygon shows the weights (kg) of a batch of parcels. Which class has the most parcels? Give its class mark.
- A. 44.5
- B. 34.5
- C. 24.5
- D. 64.5
Choose the right answer
Show the answer and working
Answer: D. 64.5
The highest point has the greatest frequency (7), at class mark 64.5.
Example 3
The histogram and frequency polygon show how many minutes a swimming squad's members trained in a week. How many are in the classes with class mark 64.5 or more?
Show the answer and working
Answer: 25 people
From class mark 64.5 on, add the frequencies of the points to its right: 25.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The frequency polygon shows the ages (in years) of a gym's members. How many are in the class with class mark 57?
Answer:
2.The frequency polygon shows the weights (kg) of a batch of parcels. Which class has the most parcels? Give its class mark.
- A. 57
- B. 72
- C. 62
- D. 67
Choose the right answer
Answer:
3.A frequency table has 6 classes: 70–74, …, 95–99. A frequency polygon adds a point with frequency 0 at each end, at the class marks and .
Fill in each blank
Answer:
4.The frequency polygon shows how many minutes a running club's members ran last week. How many members does the club have?
Answer:
5.The histogram and frequency polygon show how many minutes a swimming squad's members trained in a week. How many are in the classes with class mark 84.5 or more?
Answer:
All the answers
- 1. 6 people
- 2. A. 57
- 3. 67, 102
- 4. 24 members
- 5. 4 people
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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