Government Statisticians collect analyse and disseminate official statistics in order to meet the needs of government, business, and the public for trusted, authoritative, relevant and timely statistics, and related analysis and advice.
You need to have strong quantitative and statistical knowledge prior to starting your career as a statistician. This career provides an opportunity to directly use the statistical knowledge learnt in your social science degree.
Taking the MSc Social Statistics course at Southampton or another postgraduate taught statistical course will put you in a great position.
Useful Links:
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UK Statistics Authority- information on recruitment
Royal Statistical Society- careers information