WHO Growth Charts Data files

These files contain the L, M, and S parameters needed to generate exact percentiles and z-scores along with the percentile values for the 3rd, 5th, 10th, 25th, 50th, 75th, 90th, 95th, and 97th percentiles by sex (1=male; 2=female) and single month of age. The smoothed 85th percentile values are included in the BMI-for-age and weight-for-stature tables. Age is listed at the half month point for the entire month; for example, 1.5 months represents 1.0-1.99 months or 1.0 month up to but not including 2.0 months of age. The only exception is birth, which represents the point at birth. To obtain L, M, and S values at finer age or length/stature intervals interpolation could be used.

The LMS parameters are the median (M), the generalized coefficient of variation (S), and the power in the Box-Cox transformation (L). To obtain the value (X) of a given physical measurement at a particular z-score or percentile, use the following equation:

X = M (1 + LSZ)**(1/L), L ≠ 0

Or

X = M exp(SZ), L = 0

where the L, M, and S are the values from the appropriate table corresponding to the age in months of the child (** indicates an exponent, such that M(1+LSZ)**(1/L) means raising (1+LSZ) to the (1/L)th power and then multiplying the M; exp(X) is the exponentiation function, e to the power X). Z is the z-score that corresponds to the percentile. z-scores correspond exactly to percentiles, e.g., z-scores of -1.881, -1.645, -1.282, -0.674, 0, 0.674, 1.036, 1.282, 1.645, and 1.881 correspond to the 3rd, 5th, 10th, 25th, 50th, 75th, 85th, 90th, 95th, and 97th percentiles, respectively.

For example, to obtain the 5th percentile of weight-for-age for a 9-month-old male, we would look up the L, M and S values from the WTAGEINF table, which are L=-0.1600954, M=9.476500305, and S=0.11218624. For the 5th percentile, we would use Z=-1.645. Using the equation above, we calculate that the 5th percentile is 7.90 kg.

To obtain the z-score (Z) and corresponding percentile for a given measurement (X), use the following equation:

((X/M)**L) – 1
Z = ————————-, L≠0
LS

or

Z = ln(X/M)/S ,L=0

where X is the physical measurement (e.g. weight, length, head circumference, stature or calculated BMI value) and L, M and S are the values from the appropriate table corresponding to the age in months of the child (or length/stature). (X/M)**L means raising the quantity (X/M) to the Lth power.

For example, to obtain the weight-for-age z-score of a 9-month-old male who weighs 9.7 kg, we would look up the L, M and S values from the WTAGEINF table, which are L=-0.1600954, M=9.476500305, and S=0.11218624. Using the equation above, we calculate that the z-score for this child is 0.207. This z-score corresponds to the 58th percentile.

Z-scores and corresponding percentiles can be obtained from standard normal distribution tables found in statistics text books. Standard normal tables can also be found on the internet by doing a search on a “standard normal table.” In addition, many computer programs have pre-existing functions that convert Z-scores to percentiles and vice versa.