# Question 5:

## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| One large square $= \frac{450}{\text{"22.5"}}$ or one small square $= \frac{450}{\text{"562.5"}}$ | M1 | For attempt to count squares (accept "22.5" in [22,23] and "562.5" in [550,575]) and use 450 to obtain measure of scale |
| One large square $= 20$ cars or one small square $= 0.8$ cars or 1 car $= 1.25$ squares | A1 | For a correct calc. for 20 or 0.8 or 1.25 etc |
| No. $> 35$ mph is: $4.5 \times \text{"20"}$ or $112.5 \times \text{"0.8"}$ | dM1 | Dependent on 1st M1; for correctly counting squares for $> 35$ mph and forming suitable expression |
| $= 90$ (cars) | A1 | For 90 with no incorrect working seen; e.g. $\frac{4.5}{22.5} \times 450$ scores M1A1M1 and A1 when $= 90$ seen |

## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\bar{x} = \frac{30 \times 12.5 + 240 \times 25 + 90 \times 32.5 + 30 \times 37.5 + 60 \times 42.5}{450} = \frac{12975}{450}$ | M1 | 1st M1 for clear sensible use of midpoints; at least 3 of (12.5, 25, 32.5, 37.5, 42.5) seen |
| | M1 | 2nd M1 for expression for $\bar{x}$ with at least 3 correct terms on numerator and compatible denominator |
| $= 28.83...$ or $\frac{173}{6}$ awrt $\mathbf{28.8}$ | A1 | For awrt 28.8 (answer only is 3/3) |

## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $Q_2 = 20 + \frac{195}{240} \times 10$ | M1 | For a full expression for median using their frequencies; do not accept boundaries of 19.5 or 20.5 (M0A0) |
| $= 28.125$ awrt $\mathbf{28.1}$ | A1 | For awrt 28.1 (answer only is 2/2); use of $(n+1)$ accept 28.15 but not 28.2 |

## Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $Q_2 < \bar{x}$, so positive skew | B1ft | For correct statement about their $Q_2$ and $\bar{x}$; condone $Q_2 \approx \bar{x}$ only if $|Q_2 - \bar{x}| < 1$; do not accept argument based on shape of graph alone |
| Compatible description of skewness | dB1ft | Dependent on 1st B1; if $Q_1 = 23.4$ and $Q_3 = 33.7 \sim 33.8$ seen, allow comparison of quartiles for 1st B1 |

## Part (e):
| Answer/Working | Marks | Guidance |
|---|---|---|
| [If chose skew in (d)] **median** ($Q_2$); since the data is skewed, or median not affected by extreme values | B1 | 1st B1 for correct choice based on skewness comment in (d); if no choice made in (d) only $Q_2$ |
| Compatible supporting comment | dB1 | 2nd dB1 for a suitable compatible comment |
| [If chose symmetric in (d)] **mean** ($\bar{x}$); since it uses all the data | | |

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