# Question 3:

## Part 3(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cumulative frequency curve plotted | M1 | At least 4 points plotted within tolerance at upper bounds. Linear cf scale $0 \leqslant \text{cf} \leqslant 200$ and linear time scale $0 \leqslant t \leqslant 70$, with at least 3 values identified on each. Minimum scale uses at least $\frac{1}{2}$ the grid |
| | A1 | All points plotted correctly. Curve drawn and joined to $(0,0)$. Axes labelled cumulative frequency (cf), time ($t$) and minutes (min) – or a suitable title |

## Part 3(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 33$ | B1 FT | Must be identified. Evidence of use of graph must be seen. Strict FT $\pm \frac{1}{2}$ square on time axis |
| $[\text{IQR} =]\ 42 - 26$ | M1 | $41 \leqslant \text{UQ} \leqslant 43 - 25 < \text{LQ} \leqslant 27$. If outside of range FT $\pm \frac{1}{2}$ square on time axis |
| $16$ | A1 FT | |

## Part 3(c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Midpoints: $7.5, 20, 27.5, 35, 45, 60$; Frequencies: $18, 28, 42, 52, 36, 24$ | B1 | At least 5 correct midpoints or 5 correct frequencies seen |
| $\text{Mean} = \frac{18\times7.5 + 28\times20 + 42\times27.5 + 52\times35 + 36\times45 + 24\times60}{200}$ | M1 | Correct mean formula using their 6 midpoints (must be within class, not upper bound, not lower bound); condone 1 error and their 6 frequencies (not cumulative frequencies) |
| $= 33.65,\ 33\frac{13}{20}$ | A1 | Accept $33.7$, not $\frac{673}{20}$ |

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