Numeracy Higher June 2022 Unit 1 Q8
8. Robert’s Plants is a company that grows ornamental trees to sell in its nursery.
The histogram below shows the heights of the 80 trees in the nursery.
(a) Trees that can be sold are at least 50 cm tall.
How many trees are too short to be sold? [2]
How many trees are too short to be sold? [2]
(b) Use the histogram to give the best estimates for the answers to the following questions.
(i) What is the median height of the 80 trees?
Circle your answer. [1]
Circle your answer. [1]
47·5 cm 48 cm 50 cm 55 cm 60 cm
(ii) Calculate the inter-quartile range of the heights of the 80 trees. [6]
| Scheme | Marks | Comments |
|---|---|---|
| 40×0.3 + 10×1 OR 80 – (10×1.8 + 15×1.6 + 20×0.8) | M1 | 12 + 10 OR 80 – (18 + 24 + 16) |
| = 22 (trees) | A1 | If no marks awarded, SC1 for sight of 58 (trees greater than 50cm) from 10×1.8 + 15×1.6 + 20×0.8 |
(i)
(ii)
| Scheme | Marks | Comments |
|---|---|---|
| 60 cm | B1 |
(ii)
| Scheme | Marks | Comments |
|---|---|---|
| Search for the lower quartile (Working fwds from 40) (Working bwds from 50) 1x = 20 − 40×0.3 OR 1x = 10 − 10×0.8 | M1 | OR \(\dfrac{8}{10}\) × 10 OR \(\dfrac{2}{10}\) × 10 Needs to be unambiguous work leading towards their lower quartile |
| x = 8 OR x = 2 | A1 | Lower quartile of 48 implies M1A1 |
| Search for the upper quartile (Working fwds from 60) (Working bwds from 75) 1.6y = 20 OR 1.6y = 20 − 20×0.8 | M1 | OR \(\dfrac{20}{15 \times 1.6}\) × 15 \(\left(=\dfrac{20}{24} \times 15\right)\) OR \(\dfrac{20 - 20 \times 0.8}{15 \times 1.6}\) × 15 \(\left(=\dfrac{4}{24} \times 15\right)\) Needs to be unambiguous work leading towards their upper quartile |
| y = 12.5 OR y = 2.5 | A1 | Allow improper fractions Upper quartile of 72.5 implies M1A1 |
| (Inter-quartile range =) (60 + 12.5) – (40 + 8) or equivalent OR (75 − 2.5) – (50 − 2) or equivalent | M1 | 72.5 – 48 FT ‘their 12.5’ or ‘their 2.5’ AND FT ‘their 8’ or ‘their 2’ in an appropriate calculation provided one of the quartiles is correct and the other quartile is in the correct group (40-50 or 60-75) |
| = 24.5 (cm) | A1 | CAO |