GCSE · Data representation

Frequency polygonsExam-style questions

Turn a grouped frequency table into a frequency polygon (each frequency plotted at the midpoint of its class, the points joined with straight lines) and read one back into a table. Find the modal class, the class containing the median and an estimate of the mean from a polygon, compare two polygons on one grid in context, and spot the mistakes that cost marks.

Start practising Read the lesson

15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
The frequency polygon shows information about the times, $t$ minutes, that some students spent practising a musical instrument on Saturday.

The classes are $0 < t \le 10$ , $10 < t \le 20$ , $20 < t \le 30$ and $30 < t \le 40$ .(a) How many students are shown on the frequency polygon?

(1 mark)
(b) Find the class interval that contains the median.

(1 mark)
(c) What percentage of the students practised for more than $20$ minutes?

(2 marks)
Level 3 · 4 marksTry it
2
The frequency polygon shows information about the distances, $d$ km, that $20$ members of a walking club walked one Sunday.

The classes are $0 < d \le 4$ , $4 < d \le 8$ , $8 < d \le 12$ and $12 < d \le 16$ .(a) Work out an estimate for the mean distance walked.

(3 marks)
(b) Explain why your answer to part (a) is only an estimate.

(1 mark)
Level 3 · 4 marksTry it
3
A pizza shop records the time, $t$ minutes, it takes to deliver each of $50$ pizzas.

The classes are $0 < t \le 10$ , $10 < t \le 20$ , $20 < t \le 30$ and $30 < t \le 40$ .

The frequency polygon is not finished. It shows the first three classes only.(a) Work out the frequency of the class $30 < t \le 40$ .

(2 marks)
(b) Write down the coordinates of the point that should be plotted for the class $30 < t \le 40$ .

(1 mark)
Level 3 · 3 marksTry it
4
On sports day, $30$ Year 7 students and $30$ Year 9 students each threw a ball as far as they could.

The frequency polygons show information about the distances, $d$ metres, that they threw.

The classes are $0 < d \le 10$ , $10 < d \le 20$ , $20 < d \le 30$ and $30 < d \le 40$ .(a) How many Year 9 students threw the ball more than $20$ metres?

(1 mark)
(b) Compare the distances thrown by the Year 7 students and the Year 9 students.

Give two comparisons.

(2 marks)
Level 3 · 3 marksTry it
5
A toy car runs on a battery. The time, $t$ hours, that each of $50$ Brand A batteries and $25$ Brand B batteries lasted in the toy car was recorded.

The frequency polygons show the results. The classes are $0 < t \le 2$ , $2 < t \le 4$ , $4 < t \le 6$ , $6 < t \le 8$ and $8 < t \le 10$ .Leo says,

"Brand A batteries last longer than Brand B batteries, because the line for Brand A is higher."
(a) Explain why Leo's reason is wrong.

(1 mark)
(b) How many of the Brand B batteries lasted more than $6$ hours?

(1 mark)
(c) Which brand of battery lasted longer on average? Give a reason for your answer.

(1 mark)
Level 3 · 3 marksTry it

3 more questions on frequency polygons

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free