Higher November 2020 Paper 2 Q15
15. The mean of the data in the frequency table below is 2·7.
| \(x\) | Frequency |
|---|---|
| 1 | \(a\) |
| 2 | 5 |
| 3 | 1 |
| 4 | \(b\) |
| 5 | 2 |
| 6 | 3 |
| Total | 30 |
Work out the values of \(a\) and \(b\). [5]
You must show all your working.
| Scheme | Marks | Comments |
|---|---|---|
| \(a+b=19\) | B1 | Allow for \(a+5+1+b+2+3=30\) |
| \((a+2\times5+1\times3+4b+5\times2+6\times3)\div30=2.7\) OR \((a+4b+41)\div30=2.7\) OR \(a+2\times5+1\times3+4b+5\times2+6\times3=30\times2.7\) | M1 | |
| \(a+4b=2.7\times30-41\) or \(a+4b=40\) | M1 | FT ‘their derived 41’ |
| Complete method to solve the simultaneous equations | M1 | FT ‘their equations’ for M1 only |
| \(a=12\) and \(b=7\) | A1 | CAO |
| (5) |