## (a)
10.5 | B1 |

## (b)
$(Q_2 =) (15.5 +) \frac{\frac{1}{2} \times 30 - 14}{8} \times 3$ or $\frac{\frac{1}{2} \times 31 - 14}{8} \times 3$ | M1 |
= 15.875 or 16.0625 | A1 |

## (c)
$\bar{x} = \frac{477.5}{30} = 15.9$ (15.91⅔) [Accept $\frac{191}{12}$ or $15\frac{11}{12}$] | M1, A1 |
$\sigma = \sqrt{\frac{8603.75}{30} - x^2} = 5.78$ (accept s = 5.88) | M1A1ft, A1 |

## (d)
Since mean and median are similar (or equal or very close) a normal distribution may be suitable. [Allow mean or median close to mode/modal class] | B1 |

## (e)
$Q_3 - Q_2 (= 8) > (4.5 =) Q_2 - Q_1$ Therefore positive skew | M1, A1 |

**Notes:**
- **In parts (a) to (c)** a correct answer with no working scores full marks for that value.
- **(a)** B1 for 10.5 which may be in the table
- **(b)** M1 for a correct ratio and times 3, ignore the lower boundary for this mark
  - A1 for awrt 15.9 (if n = 30 used) or awrt 16.1 (if n+1 = 31 is used)
- **(c)** 1st M1 for attempt at $\sum fx$ (this may be seen in the table as fx: 10, 73.5, 70, 136, 82, 106 [condone 1 slip] or awrt 500) and use of $\frac{\sum fx}{\sum f}$ or a correct expression for mean.
  - 1st A1 for awrt 15.9
  - 2nd M1 for an attempt at σ or σ², can ft their mean, condone mis-labelling $\sigma^2 = \sqrt{...}$ etc. Allow use of their $\sum fx^2$ (awrt 9000)
  - 2nd A1ft for a correct expression including square root, ft their mean but not their $\sum fx^2$.
  - No label or correct label is OK but wrong label (e.g. $\sigma^2 = \sqrt{...}$) is A0
  - 3rd A1 for awrt 5.78, allow s = awrt 5.88. **SC Allow M1A1A0 for awrt 5.79 if $\bar{x}$ correct**
- **(d)** B1 for a reason implying or stating symmetry. "Time is continuous" or "evenly distributed" is B0
- **(e)** M1 for a clear reason or comparison, values not essential but comparison implying they have been found is required.
  - A1 for stating "positive skew". Condone just "positive" but "positive correlation" is A0. **Do not allow arguments based on mean and median since this part relates to a different set of data.**

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