4MA0 Foundation January 2013 Paper 1 Q17
17 A school has 60 teachers.
The table shows information about the distances, in km, the teachers travel to school each day.
| Distance (\(d\) km) | Frequency |
|---|---|
| \(0 \lt d \leqslant 5\) | 12 |
| \(5 \lt d \leqslant 10\) | 6 |
| \(10 \lt d \leqslant 15\) | 4 |
| \(15 \lt d \leqslant 20\) | 6 |
| \(20 \lt d \leqslant 25\) | 14 |
| \(25 \lt d \leqslant 30\) | 18 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the total distance travelled to school by the 60 teachers each day. (3)
| Scheme | Marks |
|---|---|
| \(25 \lt d \leqslant 30\) | B1 |
| (1) |
Notes
B1: identifies 25 \(\to\) 30 class
| Scheme | Marks |
|---|---|
| \((12 \times 2.5) + (6 \times 7.5) + (4 \times 12.5) + (6 \times 17.5) + (14 \times 22.5) + (18 \times 27.5)\) (totals: 30, 45, 50, 105, 315, 495) | M2 |
| 1040 | A1 |
| (3) |
Notes
M2: do not have to see intention to add
If not M2 then M1 for freq × consistent interval value (890 = freq × lower limit, 1190 = freq × upper limit) or 3 or more correct products stated or evaluated
A1: isw if 1040 calculated correctly and correct mean calculation follows (\(1040 \div 60 = 17.3\) or better)