Endgames Statistical Question

# The Normal distribution

BMJ 2010; 341 (Published 04 November 2010) Cite this as: BMJ 2010;341:c6085
1. Philip Sedgwick, senior lecturer in medical statistics
1. 1Section of Medical and Healthcare Education, St George’s, University of London, Tooting, London, UK
1. p.sedgwick{at}sgul.ac.uk

Researchers used a cohort study to investigate whether twins and singletons differed in academic performance during adolescence.1 A total of 7796 singletons (a 5% random sample) and 3411 twin individuals born in Denmark from 1986 to 1988 were followed from birth.

Cohort members completed a general academic test in the ninth grade of school at the age of 15 or 16. The test covered major domains of academic achievement and was scored between zero and 13. The test scores were normally distributed, with almost identical means and standard deviations (SD) for singletons (n=6575) and twins (n=2866) (mean 8.02 (SD 1.06) v mean 8.02 (SD 1.05); fig 1).

Which of the following statements, if any, are true?

• a) The histograms in fig 1 display the empirical distributions of ninth grade test scores

• b) The Normal distribution is a theoretical distribution

• c) The Normal distribution is uniquely described by its mean and standard deviation

• d) The mean …

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