Using midpoints and frequencies.
8 original questions, 31 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A histogram shows the heights of 71 trees. The table gives the frequency density for each class.
| Height (h m) | Frequency density |
|---|---|
| 0 < h ≤ 10 | 1.2 |
| 10 < h ≤ 20 | 2.5 |
| 20 < h ≤ 40 | 1.5 |
| 40 < h ≤ 50 | 0.4 |
Work out the frequency for each class and check that the total is 71.
A histogram shows the waiting times, w minutes, of 50 callers. The table gives the frequency density for each class.
| Waiting time (w minutes) | Frequency density |
|---|---|
| 0 < w ≤ 5 | 2 |
| 5 < w ≤ 10 | 4 |
| 10 < w ≤ 15 | 3 |
| 15 < w ≤ 20 | 1 |
Work out an estimate for the mean waiting time.
A histogram shows the times, t minutes, taken by 60 pupils to travel to school. The table gives the frequency density for each class.
| Time (t minutes) | Frequency density |
|---|---|
| 0 < t ≤ 10 | 1.8 |
| 10 < t ≤ 15 | 3.2 |
| 15 < t ≤ 25 | 1.4 |
| 25 < t ≤ 45 | 0.6 |
Work out an estimate for the mean time.
A histogram shows the masses, m kg, of parcels in a depot. There is no scale on the vertical axis, so the table gives the height of each bar in cm.
| Mass (m kg) | Bar height (cm) |
|---|---|
| 0 < m ≤ 2 | 1.5 |
| 2 < m ≤ 4 | 3 |
| 4 < m ≤ 8 | 2.5 |
| 8 < m ≤ 10 | 0.5 |
The bar for 2 < m ≤ 4 represents 18 parcels.
A histogram shows the journey times, d minutes, of 50 delivery drivers. The table gives the frequency density for each class.
| Time (d minutes) | Frequency density |
|---|---|
| 0 < d ≤ 4 | 2.5 |
| 4 < d ≤ 8 | 5 |
| 8 < d ≤ 12 | 3.75 |
| 12 < d ≤ 16 | 1.25 |
The table shows the frequency densities from a histogram of the waiting times, w minutes, of 40 callers to a helpline.
| Waiting time (w minutes) | Frequency density |
|---|---|
| 0 < w ≤ 4 | 2 |
| 4 < w ≤ 10 | 3 |
| 10 < w ≤ 12 | 5 |
| 12 < w ≤ 20 | 0.5 |
A histogram shows the ages, x years, of 80 members of a club. Some of the frequency densities are in the table.
| Age (x years) | Frequency density |
|---|---|
| 0 < x ≤ 10 | 2.4 |
| 10 < x ≤ 30 | 1.4 |
| 30 < x ≤ 40 | k |
| 40 < x ≤ 60 | 0.4 |
A histogram shows the times, t minutes, that 80 shoppers spent in a shop. The table gives the height of each bar in cm.
| Time (t minutes) | Bar height (cm) |
|---|---|
| 0 < t ≤ 2 | 1.5 |
| 2 < t ≤ 4 | 1 |
| 4 < t ≤ 8 | 2 |
| 8 < t ≤ 10 | 3.5 |
The bar for 4 < t ≤ 8 represents 32 shoppers.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.