Numeracy Foundation June 2018 Unit 1 Q9
9. The tables below show all of the international football results for Wales in 1984 and 1985.
1984
| 28 Feb 1984 | Scotland | 2 – 1 | Wales |
| 2 May 1984 | Wales | 1 – 0 | England |
| 22 May 1984 | Wales | 1 – 1 | Northern Ireland |
| 6 Jun 1984 | Norway | 1 – 0 | Wales |
| 10 Jun 1984 | Israel | 0 – 0 | Wales |
| 12 Sep 1984 | Iceland | 1 – 0 | Wales |
| 17 Oct 1984 | Spain | 3 – 0 | Wales |
| 14 Nov 1984 | Wales | 2 – 1 | Iceland |
1985
| 26 Feb 1985 | Wales | 1 – 1 | Norway |
| 27 Mar 1985 | Scotland | 0 – 1 | Wales |
| 30 Apr 1985 | Wales | 3 – 0 | Spain |
| 5 Jun 1985 | Norway | 4 – 2 | Wales |
| 10 Sep 1985 | Wales | 1 – 1 | Scotland |
| 16 Oct 1985 | Wales | 0 – 3 | Hungary |
Geraint says,
‘On average, the Wales international football team scored more goals per match in 1985 than in 1984.’
(a) In checking the truth of Geraint’s statement, why would it not be helpful to consider the range of the number of goals scored per match in each year? [1]
(b)
(i) By considering the mean number of goals scored per match by Wales each year, is Geraint’s statement true?
You must show calculations for each year to support your answer. [3]
You must show calculations for each year to support your answer. [3]
(ii) Give one reason why this method does not necessarily show that the Wales international football team results were better in 1985 than in 1984. [1]
| Scheme | Marks | Comments |
|---|---|---|
| Suitable reason, e.g. ‘the range is not an average’, ‘range doesn’t take all the goals into consideration’, ‘doesn’t tell you about the number of goals scored’, ‘because the range is only the difference between the highest and the lowest’ | E1 | Ignore additional comments made, irrespective of being reasonable or not Do not accept, e.g. ‘Different number of games played’, ‘Wales played more games in 1984’, ‘average is not relevant’, ‘Wales scored a different number of goals in the 2 years’, ‘Wales scored more goals in 1985’, ‘Wales might have had a different team in 1985’, ‘because the range is the difference between the highest and the lowest’, ‘to find the average you find the mean’ |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) Method to find the mean, e.g. 5 ÷ 8 or 8 ÷ 6 | M1 | Accept for 1 year shown, or 1 correct year |
| Both years correct: 1984 5/8 (goals), 1985 8/6 (goals) AND suitable conclusion e.g. 'yes', 'true', '1985 is better than 1984' | A2 | Accept equivalent correct interpretation showing understanding of comparison of the means without showing the fractions Accept 1 remainder 2 for 8/6 Do not ignore further inverse working, e.g. 8 ÷ 5 rather than 5 ÷ 8 A1 for 1 of their 2 means correct, do not ignore further inverse working Left as operations, i.e. 5÷8 and 8÷6, if no further interpretation, A0 However if further interpretation, e.g. being <1 and >1, or equivalent then award A1 Note: 1984: (1+1+1+0+0+0+0+2) ÷ 8 (= 5/8 = 0.625 goals) 1985: (1+1+3+2+1+0) ÷ 6 (= 8/6 = 1.33… goals) Accept rounding or truncation |
| (b)(ii) Reason, e.g. ‘other teams might have been stronger’, ‘don’t know about injuries’, ‘home and away goals not considered’, 'doesn't consider winning and losing', ‘Wales haven’t played against the same teams in the 2 years’, ‘they played different teams’, ‘there were different players’, ‘doesn’t consider goals against’ | E1 | Allow, e.g. ‘different number of matches’ Do not accept, e.g. ‘only looked at mean' Allow statement of different
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