Foundation November 2021 Paper 1 Q19
19 A company sells bags of toffees and bags of mints.
| Here are the numbers of sweets in 11 bags of toffees. 55 50 49 51 55 47 54 50 49 55 57 |
| Here are the numbers of sweets in 10 bags of mints. 46 47 47 48 48 50 53 54 54 54 |
The company claims that the average number of sweets per bag is at least 50
Using medians, is the company’s claim correct for each type of sweet?
You must work out the median for toffees and the median for mints. [4 marks]
Toffees
Tick a box for toffees.
- Yes
- No
Mints
Tick a box for mints.
- Yes
- No
| Answer | Mark | Comments |
|---|---|---|
| Puts toffees in order or orders the numbers to at least the sixth number from either end 47, 49, 49, 50, 50, 51 or 57, 55, 55, 55, 54, 51 or gives median of toffees as 51 | M1 | allow one error or omission on an attempt at a full list |
| Identifies 48 and 50 for mints or gives median of mints as 49 | M1 | eg circled in list or vertical line between 48 and 50 |
| 51 for toffees and 49 for mints | A1 | with no errors seen |
| Yes for toffees and No for mints | A1ft | correct decision for their values with M1M1 awarded and a single median given for each |
Additional guidance
| Ignore modes or means if medians also given, but modes or means only scores zero | |
| Beware of medians coming from only using the distinct values: 47, 49, 50, 51, 54, 55, 57 46, 47, 48 | 50, 53, 54 | M0 |
| For the A1ft, the median may be a decimal eg 47, 49, 49, 50, 50, 51, 51, 54, 55, 55, 57 median = 50.5 \(48 + 50 = 98\), \(98 \div 2 = 44\) Yes for toffees, No for mints | M1M1A0A1ft |