# Question 4:

## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Convenience or opportunity [sampling] | B1 | |

## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Quota [sampling] | B1 | For quota sampling mentioned. "Stratified", "systematic" or "random" are B0B0 |
| e.g. Take 4 people every 10 minutes | B1 | For description of how such a system might work; requires suitable strata or categories e.g. time slots, departments, gender, age groups. Suggestion of randomness is B0 |

## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Census | B1 | |

## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $[58 - 26 =]\ \mathbf{32}$ (min) | B1 | |

## Part (e):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\mu = \frac{4133}{95} = 43.505\ldots$ awrt $\mathbf{43.5}$ (min) | B1 | For a correct mean (awrt 43.5) |
| $\sigma_x = \sqrt{\frac{202294}{95} - \mu^2} = \sqrt{236.7026\ldots}$ | M1 | For correct expression for sd (including $\sqrt{\ }$) ft their mean |
| $= 15.385\ldots$ awrt $\mathbf{15.4}$ (min) | A1 | For awrt 15.4. Allow $s = 15.4667\ldots$ awrt 15.5 |

## Part (f):
| Answer | Marks | Guidance |
|--------|-------|----------|
| There are outliers in the data (or data is skew) which will affect mean and sd | B1 | For acknowledging outliers or skewness are a problem for mean and sd. "extreme values"/"anomalies" OK |
| Therefore use median and IQR | dB1 | Dependent on 1st B1, for therefore choosing median and IQR |

## Part (g):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Value of 20, LQ at 26 and outliers will not change; or state that median and upper quartile are the values that do change | B1 | For identifying 2 of these 3 groups of unchanged values or stating only $Q_2$ and $Q_3$ change |
| More values now below 40 than above so $Q_2$ or $Q_3$ will change and be lower | M1 | For explaining that median or UQ should be lower. E.g. the 2 values have moved to below 40 (or 58) and therefore more than 50% below 40 |
| Both $Q_2$ and $Q_3$ will be lower | A1 | For stating median and UQ are both lower with clear evidence of M1 scored |

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