Higher November 2021 Paper 2 Q8
8. The table shows the time, \(t\) minutes, taken by 600 people travelling to a flower show by car.
| Time, \(t\) (minutes) | Frequency |
|---|---|
| \(20 \lt t \leqslant 40\) | 68 |
| \(40 \lt t \leqslant 80\) | 186 |
| \(80 \lt t \leqslant 100\) | 238 |
| \(100 \lt t \leqslant 150\) | 108 |
(a) Calculate an estimate of the mean travelling time for these 600 people.
You must show all your working. [4]
You must show all your working. [4]
(b) Road works delayed each of these 600 people by 3 minutes.
What would the mean travelling time have been without these road works? [1]
What would the mean travelling time have been without these road works? [1]
| Scheme | Marks | Comments |
|---|---|---|
| Midpoints 30, 60, 90, 125 | B1 | |
| 30 × 68 + 60 × 186 + 90 × 238 + 125 × 108 (2040 + 11160 + 21420 + 13500 = 48120) | M1 | FT ‘their midpoints’ provided at least 3 of ‘their 4 midpoints’ lie within the appropriate group, including lower and upper bounds for the last 3 marks |
| ÷ 600 | m1 | |
| 80.2(minutes) oe | A1 | Note: final answer 79.3 follows from using the midpoints 30, 60, 90, 120 to find \(\dfrac{47580}{600}\). |
| Scheme | Marks | Comments |
|---|---|---|
| (Best estimate) 77.2(minutes) oe OR for a clear explanation that we cannot tell e.g. ‘We do not know how many values will change group’ or ‘Slightly less as a few will move to the group below’. | B1 | FT ‘their 80.2’ – 3 Do not award the mark if the explanation is contradicted by ‘the mean will be higher’. |
| (5) |