The weight of nations: an estimation of adult human biomass

BMC Public Health

Table 1 List of excluded countries due to insufficient data on BMI

Country / Territory	UN code	Adult pop. (2005)
Other non-specified areas (Taiwan)	158	18,405,317
Serbia	688	8,037,649
China, Hong Kong SAR	344	5,840,953
Puerto Rico	630	2,936,606
Occupied Palestinian Territory	275	1,928,679
Réunion	638	582,423
Montenegro	499	502,268
China, Macao SAR	446	401,495
Guadeloupe	312	338,621
Martinique	474	313,280
Western Sahara	732	301,959
French Polynesia	258	185,626
New Caledonia	540	168,610
Netherlands Antilles	530	143,172
French Guiana	254	130,255
Channel Islands	830	124,942
Guam	316	119,046
Mayotte	175	101,272
United States Virgin Islands	850	84,706
Aruba	533	79,238
TOTAL:		40,726,117

Formula for estimating the expected (average) weight (W) in a specific age-sex group where mean and variance of BMI and of height.
Using the following notation for each individual values of BMI and W: $b = (B M I - \bar{B M I}) and h = (H - \bar{H})$
The expected weight in a group of individuals would be: $\begin{array}{l} E (W) = E (B M I \times H^{2}) = E ((\bar{B M I} + b) \times {(\bar{H} + h)}^{2}) = E ((\bar{B M I} + b) \times ({\bar{H}}^{2} + h^{2} + 2 \bar{H} h)) \\ = E ({\bar{H}}^{2} \bar{B M I} + h^{2} \bar{B M I} + 2 \bar{H} h \bar{B M I} + {\bar{H}}^{2} b + h^{2} b + 2 \bar{H} h b) \\ = {\bar{H}}^{2} \bar{B M I} + E (h^{2}) \bar{B M I} + E (h) 2 \bar{H} \bar{B M I} + E (b) {\bar{H}}^{2} + E (b h^{2}) + E (h b) 2 \bar{H} \\ = {\bar{H}}^{2} \bar{B M I} + E (h^{2}) \bar{B M I} + E (b h^{2}) + E (h b) 2 \bar{H} \end{array}$
Assuming that Height and BMI are independent: $C O V (H, B M) = 0 \Rightarrow E (h b) = 0$
Assuming that the variance of Height is constant in all values of BMI: $E (b h^{2}) = 0$
Therefore the above equation simplifies to: $E (W) = \bar{B M I} \times ({\bar{H}}^{2} + V (H))$

ISSN: 1471-2458