Background: For adult physical and mental health, the population mean predicts the proportion of individuals with "high" scores. This has not previously been investigated for child mental health. It is also unclear how far symptom scores on brief questionnaires provide an unbiased method of comparing children with different individual, family or social characteristics. Methods: Subjects were 18,415 British children aged 5-16 years. Parents, teachers, and children aged 11-16 completed Strengths and Difficulties Questionnaires (SDQs) and diagnostic interviews; the latter were used to assign multi-informant clinician-rated diagnoses. We examined how closely the prevalence of child mental disorder was predicted by SDQ mean total difficulty scores, and how these mean scores compared to alternative SDQ-based summary statistics. We did this for populations defined in terms of a wide range of risk factors using one randomly selected half of the study sample. Using these results we generated SDQ prevalence estimator equations, and validated these on the second half of the study sample. Results: Mean symptom scores closely predicted the prevalence of clinician-rated child mental disorder (R[squared] = 0.89-0.95) and performed better than alternative summary statistics based on binary SDQ outcomes. The predictions of the SDQ prevalence estimators were on average only 1-2% different from the true prevalence, with no systematic tendency towards under- or overestimation. There were only a few outlier subpopulations, all relating to children with learning difficulties. Conclusion: The proportion of children with a disorder is closely predicted by mean symptom scores, highlighting the potential importance of population-wide interventions to improve child mental health. In Britain, SDQ mean total difficulty scores generally provide an accurate and unbiased method of assessing the mental health of different subgroups. SDQ prevalence estimators may facilitate presenting these research findings as proportions that are more easily interpreted by policymakers and service providers. (Contains 2 tables and 2 figures.)