Frequency density.
15 original questions, 59 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
The table shows the frequency densities for the lengths, l cm, of the worms found in a soil survey.
| Length (l cm) | Frequency density |
|---|---|
| 0 < l ≤ 5 | 1.2 |
| 5 < l ≤ 15 | 2.1 |
| 15 < l ≤ 20 | 3.0 |
| 20 < l ≤ 40 | 0.4 |
Work out the total number of worms found in the survey.
The table shows the times, t minutes, that 53 customers spent in a coffee shop.
| Time (t minutes) | Frequency | Frequency density |
|---|---|---|
| 0 < t ≤ 10 | 18 | |
| 10 < t ≤ 15 | 12 | |
| 15 < t ≤ 25 | 15 | |
| 25 < t ≤ 45 | 8 |
Complete the frequency density column.
The frequency densities for the times, t minutes, that 80 customers waited in a post office queue are shown in the table.
| Time (t minutes) | Frequency density |
|---|---|
| 0 < t ≤ 10 | 2 |
| 10 < t ≤ 30 | 1.5 |
| 30 < t ≤ 40 | 3 |
Mia says, "The 0 < t ≤ 10 class must have the most customers because its bar is tall." Is Mia correct? You must show your working.
A histogram is drawn to show the masses, m grams, of some plums. The vertical axis has no scale, so the table records the height of each bar in centimetres.
| Mass (m grams) | Bar height (cm) |
|---|---|
| 20 < m ≤ 30 | 6 |
| 30 < m ≤ 50 | 4.5 |
| 50 < m ≤ 55 | 8 |
| 55 < m ≤ 70 | 2 |
There are 24 plums with masses in the class 20 < m ≤ 30.
The table shows information about the ages, a years, of the people at a village fete.
| Age (a years) | Frequency | Frequency density |
|---|---|---|
| 0 < a ≤ 10 | 30 | 3 |
| 10 < a ≤ 30 | f | |
| 30 < a ≤ 60 | 45 | 1.5 |
The table and histogram give information about the distances, d km, that some students travel to college.
| Distance (d km) | Frequency |
|---|---|
| 0 < d ≤ 4 | 16 |
| 4 < d ≤ 6 | |
| 6 < d ≤ 10 | 18 |
| 10 < d ≤ 16 |
The bars for 0 < d ≤ 4 and 4 < d ≤ 6 are already drawn on the histogram. The bar for 4 < d ≤ 6 has frequency density 5.5.
200 people were asked how long their journey to work takes. The table shows some of the results.
| Time (t minutes) | Frequency | Frequency density |
|---|---|---|
| 0 < t ≤ 10 | 40 | 4 |
| 10 < t ≤ 30 | 60 | 3 |
| 30 < t ≤ 40 | ||
| 40 < t ≤ 60 |
25% of the people take more than 30 minutes and up to 40 minutes. All the remaining people are in the last class.
A histogram shows the times, t seconds, that 60 shoppers waited at a checkout. The table gives the frequency densities.
| Time (t seconds) | Frequency density |
|---|---|
| 0 < t ≤ 20 | 0.6 |
| 20 < t ≤ 30 | 2.0 |
| 30 < t ≤ 35 | 3.2 |
| 35 < t ≤ 50 | 0.8 |
The table shows the frequency densities for the times, t seconds, that a number of pupils took to run 100 m. A pie chart is to be drawn to show the same information.
| Time (t seconds) | Frequency density |
|---|---|
| 10 < t ≤ 20 | 0.8 |
| 20 < t ≤ 30 | 2.4 |
| 30 < t ≤ 50 | 1.1 |
| 50 < t ≤ 70 | 0.3 |
Work out the angle of the sector of the pie chart for the class 30 < t ≤ 50.
The table shows the distances, d km, cycled by 64 members of a cycling club one Sunday.
| Distance (d km) | Frequency |
|---|---|
| 0 < d ≤ 5 | 10 |
| 5 < d ≤ 15 | 30 |
| 15 < d ≤ 20 | 8 |
| 20 < d ≤ 40 | 16 |
The table shows the masses, m kg, of 50 lambs on a farm. A histogram is to be drawn.
| Mass (m kg) | Frequency | Frequency density |
|---|---|---|
| 40 < m ≤ 50 | 6 | |
| 50 < m ≤ 60 | 14 | |
| 60 < m ≤ 65 | 15 | |
| 65 < m ≤ 80 | 15 |
The histogram shows the masses, m kg, of the 40 dogs seen at a vet's surgery one week.
The table shows the speeds, s mph, of 60 vehicles passing a speed camera.
| Speed (s mph) | Frequency |
|---|---|
| 0 < s ≤ 20 | 8 |
| 20 < s ≤ 30 | 18 |
| 30 < s ≤ 40 | 24 |
| 40 < s ≤ 60 | 10 |
120 students sat a test. The table shows the frequency densities for their marks, m.
| Mark (m) | Frequency density |
|---|---|
| 0 < m ≤ 20 | 0.5 |
| 20 < m ≤ 40 | 1.5 |
| 40 < m ≤ 60 | 2 |
| 60 < m ≤ 70 | 2.5 |
| 70 < m ≤ 100 | 0.5 |
The teacher awards a certificate to the top 10% of the students.
Estimate the lowest mark a student could get and still receive a certificate.
A gym has 200 members. A histogram shows the ages, a years, of the members. Some of the information is given in the table.
| Age (a years) | Frequency | Frequency density |
|---|---|---|
| 0 < a ≤ 10 | 30 | 3 |
| 10 < a ≤ 25 | 6 | |
| 25 < a ≤ 45 | ||
| 45 < a ≤ 60 | 1 |
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.