## Q6(i)

$\text{Mean} = \frac{180.6}{12} = 15.05$ or $15.1$ | B1 for mean | 

$S_{xx} = 3107.56 - \frac{180.6^2}{12}$ or $3107.56 - 12(\text{their } 15.05)^2 = (389.53)$ | M1 for attempt at $S_{xx}$; A1 cao | 

$s = \sqrt{\frac{389.53}{11}} = 5.95$ or better | |

NB Accept answers seen without working (from calculator) | |

| TOTAL: 3 |

## Q6(ii)

$\bar{x} + 2s = 15.05 + 2 \times 5.95 = 26.95$ | M1 for attempt at either; M1 for both |

$\bar{x} - 2s = 15.05 - 2 \times 5.95 = 3.15$ | |

So no outliers | A1 for limits and conclusion FT their mean and sd | 

| TOTAL: 3 |

## Q6(iii)

New mean $= 1.8 \times 15.05 + 32 = 59.1$ | B1FT | 

New $s = 1.8 \times 5.95 = 10.7$ | M1 A1FT | 

| TOTAL: 3 |

## Q6(iv)

New York has a higher mean or 'is on average' higher (oe) | E1FT using $\bar{F}$ ($\bar{x}$ dep) | 

| TOTAL: 1 |

## Q6(v)

New York has greater spread/range/variation or SD (oe) | E1FT using $\sigma$ dep | 

| TOTAL: 1 |

## Q6(vi)

| Upper bound | 70 | 100 | 110 | 120 | 150 | 170 | 190 |
|---|---|---|---|---|---|---|---|
| Cumulative frequency | 0 | 6 | 14 | 24 | 35 | 45 | 48 |

| B1 for all correct cumulative frequencies (may be implied from graph). Ignore cf of 0 at this stage | 

[Cumulative frequency graph with points plotted and joined with smooth curve, showing cumulative frequency (0-50) vs Hours (0-200)] | G1 for linear scales (linear from 70 to 190); ignore $x < 70$; vertical: 0 to 50 but not beyond 100 (no inequality scales); G1 for labels; G1 for points plotted as (UCB, their cf). Ignore (70,0) at this stage. No mid-point or LCB plots. | 

NB all G marks dep on attempt at cumulative frequencies. | G1 for joining all of 'their points' (line or smooth curve) AND now including (70,0) | 

NB All G marks dep on attempt at cumulative frequencies | |

Line on graph at cf $= 43.2$ (soi) or used 90th percentile $= 166$ | M1 for use of 43.2; A1FT but dep on 3rd G mark earned | 

| TOTAL: 5 |

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