## Question 7:

### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Positive | B1 | |
| | **1** | |

### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Number of people $= 20\times33(000)+5\times58(000)$ | M1 | M1 first term; M1(indep) second term |
| $= 660(000)+290(000) = 950{,}000$ | A1 | NB answer of 950 scores M2A0 |
| | **3** | |

### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $a = 1810+340 = 2150$ | M1, A1 | cao 2150 or 2150 thousand (but not 215000) |
| Median = age of $1{,}385(000)^{\text{th}}$ person or $1385.5(000)$ | B1 | B1 for $1{,}385(000)$ or $1385.5$ |
| Age 30, cf $=1{,}240(000)$; age 40, cf $=1{,}810(000)$ | | |
| Estimate median $= 30+\frac{145}{570}\times10$ | M1 | M1 for attempt to interpolate $\frac{145k}{570k}\times10$ (2.54 or better suggests this) |
| Median $= 32.5$ years $(32.54\ldots)$; if no working shown then 32.54 or better needed for M1A1; if 32.5 seen with no previous working allow SC1 | A1 | cao min 1dp |
| | **3** | |

### Part (iv)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Frequency densities: $56, 65, 77, 59, 45, 17$ (accept 45.33 and 17.43 for 45 and 17) | B1 | B1 for any one correct; B1 for all correct (soi by listing or from histogram) |
| Histogram with linear scales on both axes (no inequalities) | G1 | Note: all G marks below dep on attempt at frequency density, NOT frequency |
| Heights FT their listed fds or all correct; also correct widths; all blocks joined | G1 | |
| Appropriate label for vertical scale e.g. 'Frequency density (thousands)', 'frequency (thousands) per 10 years', 'thousands of people per 10 years' (allow key), OR f.d. | G1 | |
| | **5** | |

## Question (v):

Any two suitable comments such as: | E1, E1 | Two marks for any two valid comments

- Outer London has a greater proportion (or %) of people under 20 (or almost equal proportion) | E1 |
- The modal group in Inner London is 20-30 but in Outer London it is 30-40 | E1 |
- Outer London has a greater proportion (14%) of aged 65+ | E1 |
- **All** populations in **each** age group are higher in Outer London | E1 |
- Outer London has a more evenly spread distribution or balanced distribution (ages) o.e. | E1 |

**Total: 2 marks**

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## Question (vi):

| Answer | Mark | Guidance |
|--------|------|----------|
| Mean increase $\uparrow$ | | Any one correct: B1 |
| Median unchanged $(-)$ | | Any two correct: B2 |
| Midrange increase $\uparrow$ | | Any three correct: B3 |
| Standard deviation increase $\uparrow$ | | All **five** correct: B4 |
| Interquartile range unchanged $(-)$ | | |

**Total: 4 marks**

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**TOTAL: 20 marks**