Foundation November 2018 Paper 3 Q17
17 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 | ||
|---|---|---|---|
| \(0 \lt s \le 20\) | 5 | ||
| \(20 \lt s \le 40\) | 8 | ||
| \(40 \lt s \le 50\) | 37 | ||
| \(50 \lt s \le 60\) | 47 | ||
| \(60 \lt s \le 80\) | 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 \(\Sigma mf\) where \(m\) is a value within each group 10\(\times\)5 + 30\(\times\)8 + 45\(\times\)37 + 55\(\times\)47 + 70\(\times\)3 soi by 50+240+1665+2585+210 or 4750 M1 FT dep on M1 for their 4750 \(\div\) 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 (4170) (corrected from the printed mark scheme: 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 | |