Foundation June 2022 Paper 3 Q14
14 In a dance competition, four judges award marks to each dancer.
Each judge can award 1, 2, 3, 4 or 5 marks.
The four judges’ median mark, \(m\), is put into the formula
to get the dancer’s score, \(S\).
(a) Sam is awarded marks of 4, 3, 1 and 4.
Work out Sam’s score. [3]
Work out Sam’s score. [3]
(b) Taylor gets a score of 40.
Taylor says
Taylor says
The judges must have awarded marks of 4, 4, 5 and 5
because the median is 4.5
and \(4.5 \times 10 - 5 = 40\).
Why is Taylor not correct?
Show working to support your reason. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 30 | 3 | B1 for [median =] 3.5 M1 for their median \(\times 10 - 5\) | Accept only 30 for 3 marks If 4 (mode) or 3 (mean) or other wrong value from 1 to 4 used, M1 still available |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| At least one from 1, 4, 5, 5 2, 4, 5, 5 3, 4, 5, 5 or one judge awards 1, 2 or 3 oe and 4, 5, 5 [stay the same] | 2 | B1 for four values in order with median 4.5 with one not from 1 to 5 or for one judge awards 1, 2 or 3 without mentioning 4, 5, 5 | Condone inclusion of 4, 4, 5, 5 with another correct list Accept 1 to 3 for 1, 2 or 3 and condone 4 included e.g. 1 to 4 Accept “the rest stay the same” oe for 4, 5, 5 |