The distribution of body weight for young boys age 0-3 years can be used to evaluate the physical development of a child.
Data: body weight in kilograms
|
month |
5th% |
10th% |
25th% |
50th% |
75th% |
90th% |
95th% |
|---|---|---|---|---|---|---|---|
|
0 |
2.54 |
2.78 |
3 |
3.27 |
3.64 |
3.82 |
4.15 |
|
1 |
3.16 |
3.43 |
3.82 |
4.29 |
4.75 |
5.14 |
5.38 |
|
3 |
4.43 |
4.78 |
5.32 |
5.98 |
6.56 |
7.14 |
7.37 |
|
6 |
6.2 |
6.61 |
7.2 |
7.85 |
8.49 |
9.1 |
9.46 |
|
9 |
7.52 |
7.95 |
8.56 |
9.18 |
9.88 |
10.49 |
10.93 |
|
12 |
8.43 |
8.84 |
9.49 |
10.15 |
10.91 |
11.54 |
11.99 |
|
18 |
9.59 |
9.92 |
10.67 |
11.47 |
12.31 |
13.05 |
13.44 |
|
24 |
10.54 |
10.85 |
11.65 |
12.59 |
13.44 |
14.29 |
14.7 |
|
30 |
11.44 |
11.8 |
12.63 |
13.67 |
14.51 |
15.47 |
15.97 |
|
36 |
12.26 |
12.69 |
13.58 |
14.69 |
15.59 |
16.66 |
17.28 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for body weight in kilograms =
= ((-0.000006 * ((months)^4)) + (0.0007377 * ((months)^3)) - (0.033662 * ((months)^2)) + (0.8026072 * (months)) + 2.4385737)
10th% for body weight in kilograms =
= ((-0.000008 * ((months)^4)) + (0.0009205 * ((months)^3)) - (0.039229 * ((months)^2)) + (0.8609065 * (months)) + 2.666067)
25th% for body weight in kilograms =
= ((-0.000011 * ((months)^4)) + (0.0011489 * ((months)^3)) - (0.045737 * ((months)^2)) + (0.94444289 * (months)) + 2.9444435)
50th% for body weight in kilograms =
= ((-0.000016 * ((months)^4)) + (0.0015272 * ((months)^3)) - (0.054766 * ((months)^2)) + (1.036284 * (months)) + 3.2946854)
75th% for body weight in kilograms =
= ((-0.000016 * ((months)^4)) + (0.0015725 * ((months)^3)) - (0.057231 * ((months)^2)) + (1.0910312 * (months)) + 3.6915309)
90th% for body weight in kilograms =
= (-0.000021 * ((months)^4)) + (0.0019665 * ((months)^3)) - (0.067314 * ((months)^2)) + (1.1987668 * (months)) + 3.9439275)
95th% for body weight in kilograms =
= (-0.00002 * ((months)^4)) + (0.0019164 * ((months)^3)) - (0.06713 * ((months)^2)) + (1.2146142 * (months)) + 4.2059005)
Distribution of Weight by Month
If the same data is analyzed for each month, then the percentile represented by a given weight 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.
Age 0 - 3 years, 5 to 50%ile
|
age in years |
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
0 |
74.5744670 |
-370.9007 |
465.67137 |
|
0.08 |
21.5263240 |
-120.2143 |
169.66209 |
|
0.25 |
10.5305620 |
-80.35502 |
154.04912 |
|
0.5 |
11.4926560 |
-134.0915 |
394.47192 |
|
0.75 |
12.6641000 |
-184.3957 |
675.51028 |
|
1 |
10.9348230 |
-177.0522 |
720.52022 |
|
1.5 |
6.6022349 |
-115.2368 |
503.11548 |
|
2 |
4.1042496 |
-73.07856 |
319.46719 |
|
2.5 |
3.2564507 |
-61.57435 |
283.19839 |
|
3 |
3.0926872 |
-64.76866 |
334.09184 |
Age 0 - 3 years, 51 to 95%ile
|
age in years |
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
0 |
-47.73194 |
406.68266 |
-770.0074 |
|
0.08 |
-21.5426 |
249.83756 |
-625.4028 |
|
0.25 |
-12.68309 |
201.34344 |
-700.376 |
|
0.5 |
-11.40127 |
225.28386 |
-1015.893 |
|
0.75 |
-9.973189 |
226.44153 |
-1188.366 |
|
1 |
-8.337609 |
209.26651 |
-1215.219 |
|
1.5 |
-6.166639 |
176.48147 |
-1162.968 |
|
2 |
-6.204415 |
190.50054 |
-1364.871 |
|
2.5 |
-6.521674 |
212.60027 |
-1637.347 |
|
3 |
-5.674029 |
198.50935 |
-1641.415 |
