4MA0 Higher June 2014 Paper 4R Q11
11 \(a\), \(b\), \(c\) and \(d\) are four integers.
Their mean is 8
Their mode is 7
Their median is 7.5
(a) Find the value of the largest of the four integers. (2)
(b) Find the mean value of the numbers \((2a - 3)\), \((2b - 3)\), \((2c - 3)\) and \((2d - 3)\). (2)
| Scheme | Marks |
|---|---|
| \(7 + 7 + 8 + d = 4 \times 8\) or 7, 7, 8, (\(x\)) or 4 × 8 (=32) | M1 |
| 10 | A1 |
| (2) |
Notes
A1: (accept 7, 7, 8, 10 on answer line)
| Scheme | Marks |
|---|---|
\(\dfrac{(2 \times \text{“}7\text{”} - 3) + (2 \times \text{“}7\text{”} - 3) + (2 \times \text{“}8\text{”} - 3) + (2 \times \text{“}10\text{”} - 3)}{4}\) or \(\dfrac{2 \times 32 - 12}{4}\) or 2 × 8 − 3 | M1 |
| 13 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: ft for a complete method using candidate’s 4 numbers from (a)
or
\(\dfrac{2a - 3 + 2b - 3 + 2c - 3 + 2d - 3}{4}\) oe
A1: cao