 ### Description

The distribution of body lengths for young girls age 0-3 years can be used to evaluate the physical development of a child.

Data: body length in centimeters

 month 5th% 10th% 25th% 50th% 75th% 90th% 95th% 0 45.4 46.5 48.2 49.9 51 52 52.9 1 49.2 50.2 51.9 53.5 54.9 56.1 56.9 3 55.4 56.2 57.8 59.5 61.2 62.7 63.4 6 61.8 62.6 64.2 65.9 67.8 69.4 70.2 9 66.1 67 68.7 70.4 72.4 74 75 12 69.8 70.8 72.4 74.3 76.3 78 79.1 18 76 77.2 78.8 80.9 83 85 86.1 24 81.3 82.5 84.2 86.5 88.7 90.8 92 30 86 87 88.9 91.3 93.7 95.6 96.9 36 90 91 93.1 95.6 98.1 100 101.5

Polynomial equations approximating this data were calculated in JMP, as follows:

5th% for height in centimeters =

= ((0.0000033 * ((months)^5)) - (0.00036 * ((months)^4)) + (0.0149317 * ((months)^3)) - (0.304467 * ((months)^2)) + (4.0862464 * (months)) + 45.422707)

10th% for height in centimeters =

= ((0.0000033 * ((months)^5)) - (0.000346 * ((months)^4)) + (0.0140388 * ((months)^3)) - (0.284435 * ((months)^2)) + (3.9431024 * (months)) + 46.526493)

25th% for height in centimeters =

= ((0.000003 * ((months)^5)) - (0.000321 * ((months)^4)) + (0.0133043 * ((months)^3)) - (0.275185 * ((months)^2)) + (3.8945904 * (months)) + 48.235995)

50th% for height in centimeters =

= ((0.0000031 * ((months)^5)) - (0.000328 * ((months)^4)) + (0.0133956 * ((months)^3)) - (0.273181 * ((months)^2)) + (3.8831426 * (months)) + 49.907207)

75th% for height in centimeters =

= ((0.0000034 * ((months)^5)) - (0.000366 * ((months)^4)) + (0.014993 * ((months)^3)) - (0.303274 * ((months)^2)) + (4.1465413 * (months)) + 51.03641)

90th% for height in centimeters =

= ((0.0000044 * ((months)^5)) - (0.00046 * ((months)^4)) + (0.0179516 * ((months)^3)) - (0.34331 * ((months)^2)) + (4.3988419 * (months)) + 52.036845)

95th% for height in centimeters =

= ((0.0000038 * ((months)^5)) - (0.0004 * ((months)^4)) + (0.0159112 * ((months)^3)) - (0.31463 * ((months)^2)) + (4.2743301 * (months)) + 52.929113)

Distribution of Body Length by Month

If the same data is analyzed for each month, then the percentile represented by a given height can be derived. Initially third and fourth order polynomial equations were tried, but were found to be inaccurate. Using 2 second order polynomials for above and below the 50th percentile gave equations adequate for most clinical situations.

0 to 3 Years, 5 to 50%ile

Age in years

hgt^2

hgt in cm

coefficient

0

1.6563605

-147.87480

3304.56180

0.08

1.8344027

-178.00410

4322.59110

0.25

1.5300908

-164.86440

4442.49410

0.5

1.5300908

-184.44960

5560.29880

0.75

1.5866140

-206.16170

6700.20390

1.0

1.2673323

-172.55980

5874.98010

1.5

1.0814165

-160.37050

5946.48320

2.0