A student wanted to estimate the number of dandelion plants in a field measuring 40 m by 25 m. She placed 10 quadrats, each 0.5 m × 0.5 m, randomly in the field and counted the dandelions in each.
| Quadrat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Number of dandelions | 3 | 0 | 5 | 2 | 4 | 1 | 0 | 6 | 2 | 3 |
(a) Describe how the student could place the quadrats randomly. [2]
(b) Estimate the number of dandelion plants in the field. [3]
- (a) lay out two tape measures at right angles along two edges of the field to make a grid / axes; allow divide the field into a grid of numbered squares(1)
- (a) use a random number generator / random number table to choose the coordinates / grid squares (to place each quadrat); reject 'throw the quadrat'(1)
- (b) mean = 26 ÷ 10 = 2.6 (dandelions per quadrat); allow total 26 in 2.5 m² sampled(1)
- (b) quadrat area = 0.25 m², so 2.6 ÷ 0.25 = 10.4 per m²; allow field = 1000 m² = 4000 quadrats(1)
- (b) 10.4 × 1000 = 10 400 (plants); allow 2.6 × 4000 = 10 400; correct answer with no working scores 3(1)
- Answer: (a) grid with tape measures; random numbers as coordinates (b) 10 400
- Examiner tip: A 0.5 m × 0.5 m quadrat is 0.25 m², not 0.5 m² — this slip halves the estimate.