Higher June 2025 Paper 3 Q12
12 Rob records the time he takes to drive to work every day for 80 days.
The table shows information about the results.
| Time, \(t\) (minutes) | Frequency |
|---|---|
| \(20 \leqslant t \lt 25\) | 16 |
| \(25 \leqslant t \lt 30\) | 32 |
| \(30 \leqslant t \lt 40\) | 24 |
| \(40 \leqslant t \lt 60\) | 8 |
| Total = 80 |
Last year, the mean time Rob took to drive to work was 25 minutes.
Estimate the percentage increase in the mean driving time for these 80 days. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(22.5 \times 16\) or 360 and \(27.5 \times 32\) or 880 and \(35 \times 24\) or 840 and \(50 \times 8\) or 400 or 2480 | M1 | allow one incorrect midpoint |
| (their 360 + their 880 + their 840 + their 400) \(\div\) 80 or \(2480 \div 80\) or 31 | M1 | condone bracket error seen eg \(360 + 880 + 840 + 400 \div 80\) their values must come from ‘midpoints’ within or on class bounds multiplied by correct frequencies |
| (their \(31 - 25) \div 25\ (\times 100)\) or \(6 \div 25\ (\times 100)\) or \(0.24\ (\times 100)\) or their \(31 \div 25\ (\times 100)\) or \(1.24\ (\times 100)\) or 124 | M1 | their 31 must be \(\gt 25\) |
| 24 | A1 |
Additional guidance
| \(20 \times 16 + 25 \times 32 + 30 \times 24 + 40 \times 8 = 2160\), \(2160 \div 80 = 27\), \(2 \div 25 \times 100 = 8\) | M0M1M1A0 |
| \(2480 \div 4 = 620\), \(620 - 25 = 595\), \(595 \div 25 \times 100 = 2380\) | M1M0M1A0 |
| \(2160 \div 80 = 27\), \(2 \div 25 \times 100 = 8\) | M0M0M1A0 |
| \(16 + 32 + 24 + 8 = 80\), \(80 \div 4 = 20\) cannot score, as \(20 \lt 25\) | M0M0M0A0 |