The heights (in cm) of plants in two plots are: Plot A: 42, 50, 38, 55, 47, 60; Plot B: 30, 41, 28, 45, 52, 36. Find the range and coefficient of range of each. Which plot's heights are more spread out compared with their size?
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found Six heights in each plot. To find: the range and coefficient of range of each, then compare.
2 · Write the formulas Range = L − S; coefficient of range = (L − S)/(L + S).
3 · Work out Plot A
L = 60, S = 38
Range = 60 − 38 = 22 cm
Coefficient = 22/(60 + 38) = 22/98 ≈ 0.22
4 · Work out Plot B
L = 52, S = 28
Range = 52 − 28 = 24 cm
Coefficient = 24/(52 + 28) = 24/80 = 0.30
5 · Compare 0.30 is greater than 0.22, so the heights in Plot B are more spread out compared with their size.
6 · Check and box the answer Plot A: range 22 cm, coefficient 0.22. Plot B: range 24 cm, coefficient 0.30. Plot B is more spread out.
Scoring tip: Arrange the values in order first, so L and S are easy to spot. Give the range a unit, but not the coefficient.
