Foundation June 2019 Paper 2 Q23
23 In a sport, injury time is added time played at the end of a match.
The table shows the injury time, \(t\) (minutes) played in 380 matches.
| Injury time, \(t\) (minutes) | Frequency |
|---|---|
| \(0 \lt t \leqslant 2\) | 59 |
| \(2 \lt t \leqslant 4\) | 158 |
| \(4 \lt t \leqslant 6\) | 106 |
| \(6 \lt t \leqslant 8\) | 45 |
| \(8 \lt t \leqslant 10\) | 12 |
(a) Circle the two words that describe the data. [1 mark]
- continuous
- discrete
- grouped
- ungrouped
(b) Which class interval contains the median?
You must show your working. [2 marks]
(c) What percentage of the matches had more than 6 minutes of injury time? [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| continuous grouped | B1 | both circled |
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(380 \div 2\) or \((380 + 1) \div 2\) or \(381 \div 2\) or 190 or 190.5 or 191 | M1 | oe eg \(\dfrac{59 + 158 + 106 + 45 + 12}{2}\) may be seen by the table |
| \(2 \lt t \leqslant 4\) with 190 or 190.5 or 191 seen | A1 | |
| Alternative method 2 | ||
| \(2 \lt t \leqslant 4\) with \(59 + 158 - 106 - 45 - 12 = 54\) seen | B2 | oe calculation eg \(217 - 163 = 54\) B1 \(59 + 158 - 106 - 45 - 12 = 54\) oe |
Additional guidance
| \(2 \lt t \leqslant 4\) with 190 or 190.5 or 191 not seen | M0A0 |
| Condone 2 – 4 in both or one of the spaces on answer line if 190 or 190.5 or 191 seen | M1A1 |
| Condone missing brackets if recovered | |
| Alt 2 54 with calculation not seen | B0 |
| Alt 2 \(\quad 2 \lt t \leqslant 4\) and 54 with calculation not seen | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{45 + 12}{380}\) or \(\dfrac{57}{380}\) or \(\dfrac{3}{20}\) or 0.15 or \(100 \div \dfrac{380}{57}\) or \(57 \div 3.8\) | M1 | oe proportion or calculation must use 380 |
| 15 | A1 |
Additional guidance
| \(1 - \dfrac{59 + 158 + 106}{380}\) or \(1 - \dfrac{323}{380}\) or \(1 - \dfrac{17}{20}\) or \(1 - 0.85\) | M1 |
| Correct proportion seen even if not subsequently used | M1A0 |
| Do not allow misreads of 380 | |
| Build-up eg \(10\% = 380 \div 10\) or 38 \(5\% = 38 \div 2\) or 19 \(38 + 19 = 57\) is M0A0 unless answer 15 |