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To examine whether conditions related to scarcity at the left side of the distribution (anaemia, severe chronic energy deficiency, and underweight) are as strongly related to population means as conditions of excess at the right side of the distribution (overweight and obesity).Observational study.65 countries, with nationally representative cross sectional data from 1994 to 2014 obtained from the Demographic Health Surveys.Non-pregnant women aged 20-49. Sample of 65 countries and n=524 380 for analysis of BMI; sample of 44 countries and n=316 465 for analysis of haemoglobin.The association between mean and prevalence of each category. For BMI, prevalence of severe chronic energy deficiency (SCED, BMI <16.0), underweight (BMI <18.5), overweight (BMI >25) and obese (BMI >30.) were measured; for haemoglobin, prevalence of anaemia (haemoglobin <12.0 g/dL) and severe anaemia (haemoglobin <8.0 g/dL) were examined.There was a strong association between mean BMI and prevalence of overweight (r2=0.98; r=0.99; β=8.3 (8.0 to 8.6)) and obesity (r2=0.93; r=0.97; β=4.2 (3.9 to 4.5)). For left sided conditions, a moderate to strong association was found between mean BMI and prevalence of underweight (r2=0.67; r=−0.82; β=−2.7 (−3.1 to −2.2)), and a weaker association for SCED (r2=0.38; r=−0.61; β=−0.32 (−0.43 to −0.22)). There was a moderate association between mean haemoglobin and prevalence of anaemia (r2=0.46; r=−0.68; β=−10.8 (−14.5 to −7.1)) and a weaker association with severe anaemia (r2=0.30; r=-0.55; β=−0.55 (−0.81 to −0.29)).The associations between population means and prevalence of conditions of scarcity such as low BMI and anaemia were substantially weaker than the associations of mean BMI with conditions of excesses such as overweight and obesity.