Higher November 2023 Paper 6 Q19
19 A fitness centre records how long each customer spends in the gym.
This cumulative frequency table summarises the results.
| Time (t minutes) | Cumulative frequency |
|---|---|
| \(t \leqslant 10\) | 6 |
| \(t \leqslant 20\) | 24 |
| \(t \leqslant 30\) | 35 |
| \(t \leqslant 40\) | 48 |
| \(t \leqslant 50\) | 60 |
| \(t \leqslant 60\) | 74 |
Calculate an estimate of the mean time the customers spend in the gym.
You must show your working.
You may use the table above to help present your work. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 31.6[2…] with correct working | 5 | Accept 32 with correct working Correct working requires at least evidence of B1 B1 M1 | |
| B1 for at least 4 correct frequencies from 6, 18, 11, 13, 12, 14 B1 for at least 4 correct midpoints from 5, 15, 25, 35, 45, 55 | May be implied by correct products seen 30, 270, 275, 455, 540, 770 May be implied by correct products seen 30, 270, 275, 455, 540, 770 | ||
| M1 for \(\sum mf\) using their midpoints and their frequencies soi by 30+270+275+455+540+770 or by 2340 | their midpoints must lie in the range of t for each interval Lower: [0 or 6]+180+220+390+480+700 Upper: 60+360+330+520+600+840 Allow one error in calculation their frequencies must not be the cumulative frequencies | ||
| M1dep for their \(\frac{\sum mf}{74}\) If 0 or 1 scored, instead award SC2 for final answer 31.6[2…] with no working or insufficient working If 0 scored, instead award SC1 for 2340 with no working or insufficient working | dep on first M1 | ||