Unit 3
6 marks · HardFreya measured the heights, in cm, of 60 sunflowers in her garden. The results are grouped in the table below:
| Height (cm) | Frequency |
|---|---|
| 60 ≤ h < 80 | 8 |
| 80 ≤ h < 100 | 15 |
| 100 ≤ h < 120 | 22 |
| 120 ≤ h < 140 | 12 |
| 140 ≤ h < 160 | 3 |
Estimate the mean height of the sunflowers.
State the group that contains the median height.
The group with the highest frequency is selected for a science project. The average speed at which these sunflowers grew from 0 cm to the lower bound of the group is 2 cm per day. Calculate how many days it took for them to reach the lower bound height.
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) Mean ≈ 104.67 cm
(b) 100 ≤ h < 120
(c) 40 days
Common mistakes: Mistaking lower or upper class bounds for midpoints; Incorrect selection of the median group
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Selects correct midpoints for each class
M2 (a) · 1 mark · Uses mean formula for grouped data (follow-through)
A1 (a) · 1 mark · Correct mean to nearest integer (or to 2 d.p. if shown) (follow-through)
B1 (b) · 1 mark · Correctly states the median group (follow-through)
M3 (c) · 1 mark · Divides the lower bound by speed (follow-through)
A2 (c) · 1 mark · Correct number of days: 80 ÷ 2 = 40 (follow-through)
Worked solution
a) Take midpoints: 70, 90, 110, 130, 150. Multiply by frequency and sum:
Mean = 6340 ÷ 60 = 105.7 cm (rounded to 1 d.p., within accepted tolerance).
b) Median = 30.5th value. Cumulative frequency: 8, 23, 45, 57, 60. So the 30th–31st value is in 100 ≤ h < 120.
c) For the highest frequency group: 22 (between 100 and 120), lower bound = 100. To grow from 0 to 100 cm at 2 cm/day: 100 ÷ 2 = 50 days.