Numeracy Foundation November 2017 Unit 2 Q8
8. A newspaper report claimed the following:
- 12% of the world population is left-handed.
- Twice as many men as women are left-handed.
- 30% of the world population is mixed-handed.
Mixed-handed people prefer to use the left hand for some tasks and the right hand for others. - It is very rare to be ambidextrous, that is being able to do all tasks equally well with either hand.
In 2011, Wales had a population of 3 063 000.
In 2014, Wales had a population of 3 092 000.
(a) Calculate the number of left-handed people living in Wales in 2011.
State what assumption you have made. [3]
State what assumption you have made. [3]
Assumption:
(b) In 2011, Wales had a population of 3 063 000.
1 559 000 of these people were women.
1 559 000 of these people were women.
In 2011, what percentage of the population of Wales were men?
Give your answer correct to 1 decimal place. [3]
(c) How many mixed-handed people do you think were living in Wales in 2014?
You must show your working.
Give your answer to the nearest 1000 people. [2]
You must show your working.
Give your answer to the nearest 1000 people. [2]
(d) A country of 6 million people meets all the claims given in the newspaper report.
8% of the women in this country are left-handed.
8% of the women in this country are left-handed.
There are 3 million men living in this country.
How many left-handed men would you expect there to be in this country? [4]
| Scheme | Marks | Comments |
|---|---|---|
| 0.12 × 3 063 000 or equivalent | M1 | 12% of 3 063 000 is M0, unless the required calculation (or correct response) is seen Allow M1 for sight of 0.12 × 3 063 000 with 0.3(0) × 3 063 000 only or sight of 367560 with 918 900 only or equivalent |
| 367 560 (people) | A1 | Mark final answer If no marks allow SC1 for use of 2014 data with an answer of 371 040 |
| Assumption, e.g. ‘Wales is typical’, ‘Wales has a similar population to the rest of the world’, ‘12% of people living in Wales are left-handed’, ‘newspaper is correct for Wales’ | E1 | Independent mark Do not accept, e.g. ‘367 560 people who lived in Wales were left-handed’ Allow, e.g. ‘newspaper report is correct’, |
| Scheme | Marks | Comments |
|---|---|---|
| \((100\times)\ \dfrac{3\,063\,000 - 1\,559\,000}{3\,063\,000}\) | M2 | M1 for sight of 3 063 000 -1 559 000 (= 1 504 000) |
| 49.1 (%) | A1 | CAO. Must be to 1 decimal place |
Alternative (using number of women)
| Scheme | Marks | Comments |
|---|---|---|
| \(1\ (\times 100)\ - \dfrac{1\,559\,000}{3\,063\,000}\ (\times 100)\) | M2 | |
| 49.1(%) | A1 |
If no marks, award SC1 for an answer of 50.9(%)
Allow M2, A0 for an answer of 49(%), unsupported or provided no incorrect working seen
| Scheme | Marks | Comments |
|---|---|---|
| 0.3(0) × 3 092 000 or equivalent | M1 | (= 927 600) 30% of 3 092 000 is M0, unless the required calculation (or correct response) is seen |
| 928 000 (people) | A1 | CAO. Must be to nearest 1000 If no marks allow SC1 for use of 2011 data with an answer of 919 000 (must be nearest 1000) |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 2 × 8 (%) OR use of 12% with left hand men : left hand women is 2 : 1 | M1 | Penalise incorrect place value for millions only once |
| 16 (%) | A1 | |
| 0.16 × 3 (000 000) or 0.48 | m1 | FT ‘their 16%’ provided M1 previously awarded |
| 0.48 million or 480 000 or \(4.8 \times 10^{5}\) | A1 | A0 for an answer of 0.48 Mark final answer |
Alternatives
| Scheme | Marks | Comments |
|---|---|---|
| 0.12 × 6 000 000 or 0.24 × 3 000 000 | M1 | |
| = 720 000 | A1 | |
| \(\frac{2}{3}\) × 720 000 or 720 000 - 0.08 × 3 000 000 | m1 | (FT ‘their 720 000 provided M1 previously awarded) |
| = 480 000 | A1 | |
| OR | ||
| Use of population is 50% male | M1 | (stated or implied, but not if further incorrect working) |
| 0.08 × 6 000 000 | m1 | |
| = 480 000 | A2 | (If stated as 480 000 women, then no marks, as no engagement with the question) |
| OR | ||
| 0.08 × 3 000 000 | M1 | |
| = 240 000 (left women) | A1 | (May be implied later, but needs to be clear working with left handed women if no further working) |
| × 2 | m1 | |
| = 480 000 | A1 |