Unit 3
4 marks · Normal(a) The heights (in metres) of hibiscus plants in a garden are grouped in the table below.
| Height (m) | Frequency |
|---|---|
| 0.5 ≤ h < 1.0 | 4 |
| 1.0 ≤ h < 1.5 | 7 |
| 1.5 ≤ h < 2.0 | 11 |
| 2.0 ≤ h < 2.5 | 8 |
Estimate the mean height of the plants.
(b) Write down the modal class for this data.
(c) Expand and simplify .
Estimate the mean height of the plants.
Write down the modal class for this data.
Expand and simplify .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 1.625 m
(b) 1.5 ≤ h < 2.0
(c) h^2 + 4h + 4 · must show h^2 + 4h + 4
Common mistakes: Using correct endpoints for class midpoints; Error in mean calculation; Sign error in expansion
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Finds class midpoints and multiplies by class frequency.
A1 (a) · 1 mark · Correct calculation and answer for the mean (1.625 m to 3sf).
B1 (b) · 1 mark · States correct modal class (1.5 ≤ h < 2.0).
A2 (c) · 1 mark · Expands correctly to .
Worked solution
(a) Midpoints: (0.5+1.0)/2=0.75, (1.0+1.5)/2=1.25, (1.5+2.0)/2=1.75, (2.0+2.5)/2=2.25
Mean = [4×0.75 + 7×1.25 + 11×1.75 + 8×2.25] / (4+7+11+8) = (3+8.75+19.25+18) / 30 = 49 / 30 = 1.633... ≈ 1.63 m.
(b) The modal class is 1.5 ≤ h < 2.0 (highest frequency 11).
(c) (h+2)^2 = h^2 + 4h + 4.