Handling Data 6
4 marks · NormalThe grouped frequency table shows the masses of parcels delivered in one day.
Complete the following table by calculating the class width and the frequency density for each group.
| Mass (kg) | Frequency | Class width | Frequency density |
|---|---|---|---|
| 0 < m \leq 2 | 10 | ||
| 2 < m \leq 5 | 24 | ||
| 5 < m \leq 9 | 16 |
Use your table to draw a histogram for this data. Label your axes clearly.
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) 0 < m ≤ 2: width 2, density 5; 2 < m ≤ 5: width 3, density 8; 5 < m ≤ 9: width 4, density 4 · must show Class widths: 2, 3, 4, Frequency densities: 5, 8, 4
(b) Histogram drawn with bars for each class: widths 2, 3, and 4; heights 5, 8, and 4. · must show x-axis: Mass (kg), y-axis: Frequency density, Bar heights correct: 5, 8, 4
Must show: All class widths and frequency densities correct in table, Histogram: x-axis correct classes (Mass in kg), y-axis frequency density, bars with correct heights and widths
Common mistakes: Using frequency as height instead of frequency density; Incorrect class widths
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Finds all class widths correctly: 2, 3, and 4.
A1 (a) · 1 mark · Calculates all three frequency densities correctly: 5, 8, 4.
B1 (b) · 1 mark · Draws histogram with correct bar heights to scale and axes labelled (or FT their densities) (follow-through)
B2 (b) · 1 mark · Bars have correct widths and no gaps; axes labelled including units
Worked solution
Class widths: 0 < m ≤ 2: width = 2; 2 < m ≤ 5: width = 3; 5 < m ≤ 9: width = 4
Frequency densities: 10÷2=5; 24÷3=8; 16÷4=4
Histogram: draw bars for 0–2 (height 5), 2–5 (height 8), and 5–9 (height 4), with appropriate axes labels.