## Question 5(a):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Cumulative frequencies: 12, 28, 60, 126, 146, 150 | B1 | Correct cumulative frequencies seen (may be by table or plotted accurately on graph), condone 12 not stated |
| Axes labelled 'distance (or d) [in] km' from 0 to 60 and 'cumulative frequency' (or cf) from 0 to 150 | B1 | |
| At least 5 points plotted at upper end points for $d$ | M1 | Allow upper boundary $\pm0.5$, condone $0-4$ interval inaccurate, no scale break on axis. Not bar graph/histogram unless clear indication of upper end point only of each bar |
| All plotted correctly at correct upper end points (4.5 etc.) | A1 | Both scales linear ($0\leqslant d\leqslant60$, $0\leqslant\text{cf}\leqslant150$), curve drawn accurately joined to (0,0), cf line>150, no daylight if >150 |

## Question 5(b):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $70\%$ of $150 = 105$ | M1 | 105 seen or implied by indication on grid |
| Approx. 27 | A1 FT | Strict FT *their* increasing cumulative frequency graph, use of graph must be seen. If no clear evidence of use of graph: SC B1 FT correct value from *their* increasing cumulative frequency graph |

## Question 5(c):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Midpoints: 2.25, 7.5, 15.5, 25.5, 35.5, 50.5 | B1 | At least 5 correct midpoints seen |
| $\text{Mean} = \frac{2.25\times12+7.5\times16+15.5\times32+25.5\times66+35.5\times20+50.5\times4}{150} = \frac{27+120+496+1683+710+202}{150}$ | M1 | Using 6 midpoint attempts (e.g. $2.25\pm0.5$), condone one error not omission, multiplied by frequency, accept unevaluated, denominator either correct or *their* $\Sigma$ frequencies |
| $\left[=\frac{3238}{150}\right] = 21.6,\ 21\frac{44}{75}$ | A1 | Evaluated, WWW, accept $21.5[866\ldots]$ |