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 |
ICD-10InfoICD-10: , |
