5 A survey of all the households on an estate is undertaken to provide information on the number of children per household.
The results, for the 99 households with children, are shown in the table.
| Number of children \(( \boldsymbol { x } )\) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Number of households \(( \boldsymbol { f } )\) | 14 | 35 | 25 | 13 | 9 | 2 | 1 |
- For these 99 households, calculate values for:
- the median and the interquartile range;
- the mean and the standard deviation.
- In fact, 163 households were surveyed, of which 64 contained no children.
- For all 163 households, calculate the value for the mean number of children per household.
- State whether the value for the standard deviation, when calculated for all 163 households, will be smaller than, the same as, or greater than that calculated in part (a)(ii).
- It is claimed that, for all 163 households on the estate, the number of children per household may be modelled approximately by a normal distribution.
Comment, with justification, on this claim. Your comment should refer to a fact other than the discrete nature of the data.
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