4MA0 Higher January 2013 Paper 3 Q6
6 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 → 30 class
| Scheme | Marks |
|---|---|
| (12 x 2.5) + (6 x 7.5) + (4 x 12.5) + (6 x 17.5) + (14 x 22.5) + ( 18 x 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 x consistent interval value (890 = freq x lower limit, 1190 = freq x upper limit) or 3 or more correct products stated or evaluated
A1: isw if 1040 calculated correctly and correct mean calculation follows (1040 ÷ 60 = 17.3 or better)