4MA0 Foundation January 2015 Paper 2R Q22
22 The table gives information about the number of vehicles passing a point on a road in each of 70 intervals of equal length.
| Number of vehicles | Frequency |
|---|---|
| 1 to 5 | 8 |
| 6 to 10 | 10 |
| 11 to 15 | 18 |
| 16 to 20 | 20 |
| 21 to 25 | 10 |
| 26 to 30 | 4 |
Calculate an estimate for the mean.
(4)
| Scheme | Marks |
|---|---|
| 3×8 + 8×10 + 13×18 +18×20 + 23×10 + 28×4 or 24 + 80 + 234 + 360 + 230 + 112 or 1040 | M1 |
| M1 | |
\(\dfrac{3\times8 + 8\times10 + 13\times18 + 18\times20 + 23\times10 + 28\times4}{8 + 10 + 18 + 20 + 10 + 4}\) or “1040” ÷ (8+10+18+20+10+4) | M1 |
| 14.9 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: finds products f × x consistently within intervals (inc end points) allow 1 error
NB. products do not have to be evaluated
M1: (dep on first M1) –uses midpoints
M1: (dep on first M1) Σfx ÷Σf
A1: 14.8 − 14.9 or \(14\frac{6}{7}\)
Accept 15 if full working shown
The printed mark scheme gives this question a total of 5 marks; the question paper and the four marks above give 4.