# Question 6:

## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean, median, average, marks, results score: on P2 ($y$) is lower than P1($x$) | B1 | One of these 5 terms seen for 1st B1 |
| Spread, dispersion, range, st. dev, var(iance): on P2 is more than P1 | B1 | **(2)** |

## Part (b)(i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| e.g. (38, 0) doesn't follow the pattern/trend or out of range of other points, or far from (best fit) line / other points | B1 | Suitable explanation; saying "extreme point" is B0 |

## Part (b)(ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| The student was absent when paper 2 was taken | B1 | e.g. teacher didn't mark it, wrongly recorded/plotted **(2)** |

## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| New $\bar{x} = \frac{35.75 \times 16 - 38}{15} = \frac{534}{15} = \textbf{35.6}$ | M1, A1 | M1 for correct method; list requires $\Sigma x = 534$ and $\div 15$; A1 for 35.6 or e.g. $35\frac{3}{5}$ |
| New $\bar{y} = \frac{25.75 \times 16}{15} = 27.4\dot{6}$ awrt **27.5** (allow $\frac{412}{15}$) | B1 | B1 for awrt 27.5 **(3)** |

## Part (d)(i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| New $\sum xy = 15837 - 38 \times 0$ so no change | B1 | For explanation with sight of "$38 \times 0$"; e.g. for (38, 0) or omitted point, $xy = 0$ |

## Part (d)(ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $S_{xy} = 15837 - \frac{(35.75 \times 16 - 38)(25.75 \times 16)}{15}$ or $-\frac{\text{"534"} \times \text{"412"}}{15}$ or $-\frac{220008}{15}$ | M1 | For a correct expression (can ft their 534 and their 412 if stated in (c)) |
| $= \textbf{1169.8}$ (*) | A1cso | Dependent on M1 with no incorrect working; may be seen in (e) **(3)** |

## Part (e)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $r = \frac{1169.8}{\sqrt{965.6 \times 1561.7}} = 0.9526079\ldots$ awrt **0.953** | M1, A1 | M1 for correct method (implied by ans = awrt 0.95); A1 for awrt 0.953 **(2)** |

## Part (f)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $b = \frac{1169.8}{965.6}\ [= 1.21147\ldots]$ | M1 | 1st M1 for correct expression for $b$ |
| $a = \text{"27.5"} - \text{"b"} \times \text{"35.6"}\ [= -15.6618\ldots]$ | M1 | 2nd M1 for correct expression for $a$ (ft means in (c)) |
| $y = -15.6/7 + 1.2x$; $b$ = awrt **1.2**, $a$ = awrt **$-15.6$ or $-15.7$** | A1, A1 | $a$ and $b$ must be in an $x, y$ equation; 1st A1 for $b$, 2nd A1 for $a$ **(4)** |

## Part (g)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Value of $r$ increased from 0.746 to 0.953 so points lie closer to a straight line | B1 | Suitable comment e.g. linear relationship **stronger** or stronger linear correlation **(1)** |

## Part (h)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $y = \text{"1.21..."} \times 38 - \text{"15.66..."}$ or awrt **30** | B1ft | ft for awrt 30 or ft expression using $x = 38$ in their equation (need not be evaluated) **(1)** |

**[18 marks total]**