Handling Data 4

3 marks · Normal

A coin is tossed 10 times. The results are as follows:

Coin toss results
Toss number	1	2	3	4	5	6	7	8	9	10
Result	H	H	T	H	T	T	H	H	T	T

a) Plot a relative frequency diagram for getting a head after each toss (on the vertical axis, plot the relative frequency of heads after each toss).

b) What value does the experimental probability appear to be approaching?

(a)

Draw a relative frequency diagram (graph) for heads after each toss.

[2 marks]

(b)

What value does the probability appear to be approaching?

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) — · must show Plot for tosses 1 to 10, with cumulative frequency for heads divided by toss number

(b) 0.5

Must show: Graph: x-axis (toss number), y-axis (relative frequency), points for each toss

Also accept: Around 0.5

Common mistakes: Using frequencies not relative frequencies on graph; Plotting only last toss

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Correct calculation of cumulative relative frequency for each toss.

A1 (a) · 1 mark · Accurate plot of relative frequency against toss number (line or points).

B1 (b) · 1 mark · States value approaches 0.5.

Worked solution

Heads after each toss: 1,2,2,3,3,3,4,5,5,5

Relative frequencies: 1/1, 2/2, 2/3, 3/4, 3/5, 3/6, 4/7, 5/8, 5/9, 5/10

Cumulative relative frequencies
Toss	1	2	3	4	5	6	7	8	9	10
Rel. freq.	1	1	0.67	0.75	0.60	0.50	0.57	0.63	0.56	0.50

Relative frequency diagram

b) The value appears to approach 0.5, as expected for a fair coin.