Relative Frequency worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 35 marks Sheet 1

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4 marks
A spinner can land on white, black, orange or purple. The spinner is spun 100 times.

The table gives the results.

Colour White Black Orange Purple

Frequency 19 36 11 34

(a)
Calculate the relative frequency of white. Give your answer as a decimal.

(b)
The spinner is spun 200 more times. Estimate the number of times it will land on white.
4 marks
A drawing pin is dropped onto a table many times.

Out of \(50\) drops, it lands point up \(14\) times.

(a)
Calculate the relative frequency that it lands point up.

Give your answer as a fraction in its simplest form.

(b)
Calculate the relative frequency as a percentage.
3 marks
Amara wants to test whether a coin is fair. She flips the coin 200 times.

It lands on heads 80 times.

(a)
Work out the relative frequency of heads. Give your answer as a decimal.

(b)
Do you think the coin is fair? Give a reason for your answer.
3 marks
A bag of counters was tested 340 times.

The relative frequency of green was \(0.35\).

(a)
Work out how many times the counter taken was green.

(b)
Work out how many times it was something else.
4 marks A spinner has sections coloured gold, silver, bronze and grey. It was spun 100 times. The table shows the relative frequency of each colour.

Colour Relative frequency

gold 0.15

silver 0.35

bronze 0.2

grey

(a)
Work out the relative frequency of grey.

(b)
Calculate how many times the spinner landed on grey.
4 marks
Rosie and Kofi are testing the same spinner. They each want to estimate the probability that it lands on red.

Rosie spins it 30 times. It lands on red 18 times.

Kofi spins it 70 times. It lands on red 14 times.

(a)
Whose results give the more reliable estimate of the probability? Give a reason for your answer.

(b)
They put all of their results together. Use all 100 spins to work out the best estimate of the probability that the spinner lands on red.
3 marks
A counter is taken from a bag and put back a number of times.

It landed on grey \(84\) times.

The relative frequency of landing on grey is \(0.3\).

(a)
Calculate how many picks there were altogether.

(b)
Work out the relative frequency of not landing on grey.
3 marks
Does the line have to be stopped?

You must show your working.
3 marks
Do {poss} results support the maker's claim?

You must show your working.
4 marks A spinner is spun again and again. The table shows the relative frequency of red after different numbers of spins.

Number of spins Relative frequency of red

20 0.5

50 0.26

100 0.39

200 0.35

(a)
Write down the best estimate of the probability that the spinner lands on red.

(b)
Describe what happens to the relative frequency as the number of spins increases.

(c)
Work out how many times the spinner landed on red in the 200 spins.

Colour	White	Black	Orange	Purple
Frequency	19	36	11	34

Colour	Relative frequency
gold	0.15
silver	0.35
bronze	0.2
grey

Number of spins	Relative frequency of red
20	0.5
50	0.26
100	0.39
200	0.35

Answers

(a) \(0.19\)
(b) \(38\)
(a) \(\frac{7}{25}\)
(b) \(28\%\)
(a) \(0.4\)
(b) No — the relative frequency of 0.4 is a long way from 0.5, so the coin looks biased.
(a) \(119\)
(b) \(221\)
(a) \(0.3\)
(b) \(30\)
(a) Kofi — Kofi did 70 spins and Rosie did only 30, and the more trials there are the closer the relative frequency is likely to be to the true probability.
(b) \(0.32\)
(a) \(280\ \text{picks}\)
(b) \(0.7\)
Yes — the relative frequency is \(0.08\), which is 8%, and that is more than 4%.
The relative frequency is \({rf:dec}\), or {seenpct}%, against the claimed {claimpct}% — so {verdict}.
(a) \(0.35\)
(b) It settles down, getting closer to \(0.35\) as the number of spins increases.
(c) \(70\)

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