Higher November 2018 Paper 6 Q2
2 The police record the speed of vehicles passing a speed checkpoint.
The speeds are recorded in the table below.
| Speed (s mph) | Number of vehicles | ||
|---|---|---|---|
| \(0 \lt s \leqslant 20\) | 5 | ||
| \(20 \lt s \leqslant 40\) | 8 | ||
| \(40 \lt s \leqslant 50\) | 37 | ||
| \(50 \lt s \leqslant 60\) | 47 | ||
| \(60 \lt s \leqslant 80\) | 3 |
(a) Calculate an estimate of the mean speed of the vehicles. [4]
(b) Explain why it is not possible to use the information from this table to calculate the exact value of the mean speed. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 47.5 | 4 | B1 for at least four of 10, 30, 45, 55, 70 M1 FT for Σmf where m is a value within each group 10×5 + 30×8 + 45×37 + 55×47 + 70×3 soi by 50 + 240 + 1665 + 2585 + 210 or 4750 M1 FT dep on M1 for their 4750 ÷ their (5 + 8 + 37 + 47 + 3) | May be implied by four correct products or 4750 FT their “midpoints” seen. M1 may be implied by Lower: 0 + 160 + 1480 + 2350 + 180 (4180) Upper: 100 + 320 + 1850 + 2820 + 240 (5330) Allow one error in calculation. Expect 100 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Exact speeds for each vehicle are not recorded oe | 1 | Do not accept, “Because the mid-point is used” or comments on the method used. Accept e.g.: Specific speeds not given or We don’t know the speeds The exact speed isn’t given | |