Higher June 2023 Paper 1 Q18
18 The incomplete table and incomplete histogram give information about the times, in minutes, that 140 people waited at a station for a train.
| Time (\(t\) minutes) | Frequency |
|---|---|
| \(0 \lt t \leqslant 5\) | 23 |
| \(5 \lt t \leqslant 15\) | |
| \(15 \lt t \leqslant 30\) | |
| \(30 \lt t \leqslant 40\) | 18 |
| \(40 \lt t \leqslant 60\) | 14 |
Complete the table and the histogram.
(4)
| Scheme | Marks |
|---|---|
| 140 – (23 + 18 + 14) (= 85) and state the area of the 2 given bars, eg 34 (1 cm) squares or 8.5 large squares or 850 small squares oe OR 23 ÷ 5 (= 4.6 oe) or 18 ÷ 10 (= 1.8 oe) or 14 ÷ 20 (= 0.7 oe) | M1 |
| Use of frequency density for the given bars eg “85” ÷ 34 = 2.5 [(1 cm) square = 2.5 people] or “85” ÷ 8.5 = 10 [1 large square = 10 people] or “85” ÷ 850 = 0.1 [1 small square = 0.1 people] or 10 small squares = 1 person OR 23 ÷ 5 (= 4.6 oe) and 18 ÷ 10 (= 1.8 oe) and 14 ÷ 20 (= 0.7 oe) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(5 \lt t \leqslant 15\) has frequency 25 \(15 \lt t \leqslant 30\) has frequency 60 Bars of 4.6, 1.8, 0.7 correctly drawn to scale | A2 |
| (4) | |
| (4 marks) |
Notes
M1: or 2 correct values in the table
or 2 or 3 correct bars
A2: (A1 for 4 of
\(5 \lt t \leqslant 15\) has frequency 25
\(15 \lt t \leqslant 30\) has frequency 60
bar of 4.6,
bar of 1.8,
bar of 0.7)