Higher June 2017 Paper 3 Q13
13 In a class of 28 students
the mean height of the 12 boys is 1.58 metres
the mean height of all 28 students is 1.52 metres.
Work out the mean height of the girls. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(12 \times 1.58\) or 18.96 or \(28 \times 1.52\) or 42.56 | M1 | |
| \(28 \times 1.52 - 12 \times 1.58\) or their 42.56 – their 18.96 or 23.6 | M1dep | oe |
| their \(23.6 \div (28 - 12)\) or their \(23.6 \div 16\) | M1dep | oe dep on M1 M1 |
| 1.475 or 1.48 | A1 | |
| Alternative method 2 | ||
| \(16x + 12 \times 1.58\) or \(16x + 18.96\) or \(28 \times 1.52\) or 42.56 | M1 | |
| (\(16x =\)) their 42.56 – their 18.96 or (\(16x =\)) 23.6 | M1dep | oe |
| their \(23.6 \div (28 - 12)\) or their \(23.6 \div 16\) | M1dep | oe dep on M1 M1 |
| 1.475 or 1.48 | A1 | |
Additional guidance
| \(23.6 \div 16 = 1.475 = 1.5\) | M1M1M1A1 |
| \(23.6 \div 16 = 1.5\) | M1M1M1A0 |
| \(23.6 \div (28 - 12)\) \(23.6 \div 14\) | M1M1M1A0 |
| \(23.6 \div 14\) | M1M1M0A0 |
| Beware use of 0.06 eg \(\;1.58 - 1.52 = 0.06\) | M0 |