4MA0 Higher June 2015 Paper 4R Q5
5 Jordan’s school awards certificates for outstanding work.
The table shows information about the numbers of certificates awarded in Jordan’s class during a term.
| Number of certificates | Number of students |
|---|---|
| 0 | 4 |
| 1 | 9 |
| 2 | 7 |
| 3 | 1 |
| 4 | 6 |
| 5 | 3 |
(a) Work out the median number of certificates awarded. (2)
(b) Work out the interquartile range of the numbers of certificates awarded. (3)
| Scheme | Marks |
|---|---|
\(\dfrac{4 + 9 + 7 + 1 + 6 + 3}{2}\) or \(\dfrac{(4 + 9 + 7 + 1 + 6 + 3) + 1}{2}\) or \(\dfrac{30}{2}\) or \(\dfrac{31}{2}\) or 15 or \(15\dfrac{1}{2}\) | M1 |
| 2 | A1 |
| (2) |
Notes
M1: Condone 1 omission
Eg \(\dfrac{9 + 7 + 1 + 6 + 3}{2}\)
Accept a clear intention to list the numbers in order and find the centre of the list.
| Scheme | Marks |
|---|---|
\(\dfrac{4 + 9 + 7 + 1 + 6 + 3}{4}\) or \(\dfrac{(4 + 9 + 7 + 1 + 6 + 3) + 1}{4}\) or \(\dfrac{30}{4}\) oe (= 7.5) or \(\dfrac{31}{4}\) oe (= 7.75) or 8 or \(3 \times \dfrac{\text{"}30\text{"}}{4}\) oe (= 22.5) or \(3 \times \dfrac{\text{"}31\text{"}}{4}\) oe (= 23.25) or 23 | M2 |
| 3 | A1 |
| (3) |
Notes
M2: For Lower quartile = 1 AND Upper quartile = 4
Accept a correct ordered list of the 30 numbers with both quartiles clearly identified in the correct position.
M1 for Lower quartile = 1 or Upper quartile = 4 or
Accept a correct ordered list of the 30 numbers with the position of one of the quartiles clearly identified in the correct position.