4MA0 Higher January 2015 Paper 4R Q6
6 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 |
(a) Write down the modal class interval. (1)
(b) Calculate an estimate for the mean. (4)
| Scheme | Marks |
|---|---|
| 16 to 20 | B1 |
| (1) |
Notes
B1: Accept any unambiguous notation e.g. 16-20
| 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 | |
\(\dfrac{3 \times 8 + 8 \times 10 + 13 \times 18 + 18 \times 20 + 23 \times 10 + 28 \times 4}{8 + 10 + 18 + 20 + 10 + 4}\) or “1040” ÷ (8+10+18+20+10+4) | M1 |
| 14.9 | A1 |
| (4) | |
| (5 marks) |
Notes
M1: finds products \(f \times x\) 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) \(\Sigma fx \div \Sigma f\)
A1: 14.8 – 14.9 or \(14\dfrac{6}{7}\)
Accept 15 if full working shown