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National Curriculum: Probability and Statistics - KS3 - Exemplification

Created on 24 October 2013 by ncetm_administrator
Updated on 04 June 2014 by ncetm_administrator


Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement


Example A

A box contains bricks which are orange or blue or brown or yellow.
Damion is going to choose one brick at random from the box.

The table shows each of the probabilities that Damion will choose an orange brick or a brown brick or a yellow brick.

Colour Orange Blue Brown Yellow
Probability 0.32   0.20 0.19

Work out the probability that Damion will choose a blue brick.

Example B

Two boxes each contain a different number of black and blue ink pens.


Box 1 (Bikko) has 7 black and 11 blue ink pens.

Box 2 (Stylo) has 5 black and 7 blue ink pens.

Kylie picks a pen at random from a box. From which box is she more likely to select a blue pen? Why?

Example C

Trishane designs a game.
It costs £1.20 to play the game.

The probability of winning the game is 310

The prize for each win is £2.50
150 people play the game.

Work out an estimate of the profit that Trishane should expect to make.

Example D

Two coins are thrown at the same time. There are four possible outcomes:


How many possible outcomes are there if:

  1. three coins are used?
  2. four coins are used
  3. five coins are used?


Example E

Three children have a mean age of 10.

The range of their ages is 6.

Give two sets of possible ages for the children.

Example G

20 students scored goals for the school hockey team last month. The table gives information about the number of goals they scored.

Goals scored Number of students
1 8
2 4
3 5
4 3
  1. Write down the modal number of goals scored.
  2. Work out the range of the number of goals scored.
  3. Work out the mean number of goals scored.

Example H

In a survey, some students were asked what their favourite leisure activity was.


Their answers were used to draw this pie chart. pie chart
  1. Write down the fraction of the students who answered “Television”.
    Write your answer in its simplest form.
    12 students answered “Reading”.
  2. Work out the number of students who took part in the survey.
  3. How many answered “Sport”?

Example I

Here is a scatter graph. One axis is labelled “Height”.

scatter graph
  1. From the list below, choose the most appropriate label for the other axis.
    • length of hair
    • number of sisters
    • length of legs
    • GCSE French mark
  2. Describe the correlation shown on this graph. Explain why you think this.



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