The distribution of body lengths for young boys 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 |
46.4 |
47.5 |
49 |
50.5 |
51.8 |
53.5 |
54.4 |
|
1 |
50.4 |
51.3 |
53 |
54.6 |
56.2 |
57.7 |
58.6 |
|
3 |
56.7 |
57.7 |
59.4 |
61.1 |
63 |
64.5 |
65.4 |
|
6 |
63.4 |
64.4 |
66.1 |
67.8 |
69.7 |
71.3 |
72.3 |
|
9 |
68 |
69.1 |
70.6 |
72.3 |
74 |
75.9 |
77.1 |
|
12 |
71.7 |
72.8 |
74.3 |
76.1 |
77.7 |
79.8 |
81.2 |
|
18 |
77.5 |
78.7 |
80.5 |
82.4 |
84.3 |
86.6 |
88.1 |
|
24 |
82.3 |
83.5 |
85.6 |
87.6 |
89.9 |
92.2 |
93.8 |
|
30 |
87 |
88.2 |
90.1 |
92.3 |
94.6 |
97 |
98.7 |
|
36 |
91.2 |
92.4 |
94.2 |
96.5 |
98.9 |
101.4 |
103.1 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for height in centimeters =
= ((0.0000024 * ((months)^5)) - (0.000276 * ((months)^4)) + (0.0125091 * ((months)^3)) - (0.0283668 * ((months)^2)) + (4.1308165 * (months)) + 46.475371)
10th% for height in centimeters =
((0.0000022 * ((months)^5)) - (0.000255 * ((months)^4)) + (0.0117252 * ((months)^3)) - (0.271785 * ((months)^2)) + (4.0761928 * (months)) + 47.516595)
25th% for height in centimeters =
= ((0.0000034 * ((months)^5)) - (0.000369 * ((months)^4)) + (0.0152959 * ((months)^3)) - (0.315487 * ((months)^2)) + (4.2560769 * (months)) + 49.03369)
50th% for height in centimeters =
= ((0.0000036 * ((months)^5)) - (0.000383 * ((months)^4)) + (0.015837 * ((months)^3)) - (0.324105 * ((months)^2)) + (4.3236754 * (months)) + 50.557971)
75th% for height in centimeters =
= ((0.0000052 * ((months)^5)) - (0.000537 * ((months)^4)) + (0.0210058 * ((months)^3)) - (0.395614 * ((months)^2)) + (4.6958102 * (months)) + 51.856726)
90th% for height in centimeters =
= ((0.0000044 * ((months)^5)) - (0.000462 * ((months)^4)) + (0.0183207 * ((months)^3)) - (0.356203 * ((months)^2)) + (4.5313743 * (months)) + 53.531472)
95th% for height in centimeters=
= ((0.000004 * ((months)^5)) - (0.00042 * ((months)^4)) + (0.0169116 * ((months)^3)) - (0.336706 * ((months)^2)) + (4.4751708 * (months)) + 54.448242)
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 |
2.1719982 |
-199.5039 |
4585.7866 |
|
0.08 |
1.8048251 |
-178.8858 |
4436.5734 |
|
0.25 |
1.6248840 |
-181.2205 |
5056.4876 |
|
0.5 |
1.6248840 |
-202.9939 |
6343.6060 |
|
0.75 |
1.7022011 |
-228.2909 |
7657.6283 |
|
1 |
1.5040825 |
-211.9857 |
7471.7798 |
|
1.5 |
1.3344506 |
-204.1846 |
7814.2288 |
|
2 |
1.1693594 |
-190.2422 |
7741.7320 |
|
2.5 |
0.9598316 |
-163.5627 |
6969.8213 |
|
3 |
0.8580308 |
-152.4731 |
6773.5848 |
0 to 3 years, 51 to 95%ile
|
Age in years |
hgt^2 |
hgt in cm |
coefficient |
|---|---|---|---|
|
0 |
-2.635121 |
287.691660 |
-7757.814 |
|
0.08 |
-1.826629 |
218.028120 |
-6408.868 |
|
0.25 |
-1.190374 |
161.135190 |
-5351.538 |
|
0.5 |
-1.267332 |
187.616000 |
-6844.720 |
|
0.75 |
-1.624136 |
251.928410 |
-9674.425 |
|
1 |
-1.712555 |
278.013820 |
-11188.640 |
|
1.5 |
-1.266565 |
223.721470 |
-9784.688 |
|
2 |
-0.916428 |
173.486250 |
-8114.923 |
|
2.5 |
-0.911607 |
181.118710 |
-8900.942 |
|
3 |
-0.833547 |
173.163950 |
-8898.052 |
ICD-10: ,
