4MA0 Foundation June 2015 Paper 1 Q16
16 \(w\), \(x\), \(y\) and \(z\) are 4 integers written in order of size, starting with the smallest.
The mean of \(w\), \(x\), \(y\) and \(z\) is 13
The sum of \(w\), \(x\) and \(y\) is 33
(a) Find the value of \(z\). (2)
Given also that the range of \(w\), \(x\), \(y\) and \(z\) is 10
(b) work out the median of \(w\), \(x\), \(y\) and \(z\). (2)
| Scheme | Marks |
|---|---|
4 × 13 (= 52) or \(\dfrac{w + x + y + z}{4} = 13\) or 4 × 13 – 33 | M1 |
| 19 | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(z - w = 10\) or \(w = 9\) or \(w = \text{“}19\text{”} - 10\) or \(x + y = 33 - 9 = 24\) | M1 |
| 12 | A1 |
| (2) | |
| Total 4 marks |
Notes
M1: ft from (a)
(can be implied by 9, \(x\), \(y\), 19 OR \(w\), \(x\), \(y\), \(z\) with \(x + y = 24\))
A1: cao