Higher November 2020 Paper 3 Q12
12 Here is some information about 26 houses.
\(a\), \(b\) and \(c\) are all different numbers.
| Number of bedrooms | Number of houses |
|---|---|
| 1 | 7 |
| 2 | \(a\) |
| 3 | \(b\) |
| 4 | \(c\) |
| 5 | 8 |
The median number of bedrooms is 3.5
Work out a possible set of values for \(a\), \(b\) and \(c\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(a = 2\) and \(b = 4\) and \(c = 5\) or \(a = 4\) and \(b = 2\) and \(c = 5\) or \(a = 0\) and \(b = 6\) and \(c = 5\) | B3 | B2 \(a + b = 6\) with integer values of \(a \geqslant 0\) and \(b \geqslant 1\) B1 \(c = 5\) or \(a + b + c = 11\) with integer values of \(a \geqslant 0\) and \(b \geqslant 0\) and \(c \geqslant 0\) or 13th value = 3 and 14th value = 4 stated or correct median position indicated on a list |
Additional guidance
| Values may be seen alongside or in the table | |
| Blank answer line does not indicate zero for that value eg \(a =\) _____ \(b = 6\) \(c = 5\) | B1 |
| \(a = 2\) \(b = 6\) \(c = 5\) | B1 |
| \(a = 11\) \(b = 0\) \(c = 0\) | B1 |
| \(a = 6\) \(b = 0\) \(c = 5\) | B1 |
| \(a = 6\) \(b = 0\) \(c = 3\) | B0 |