The distribution of weight for boys age 2-18 years can be used to evaluate the physical development of a child.
Data: weight in kilograms.
|
year |
5th% |
10th% |
25th% |
50th% |
75th% |
90th% |
95th% |
|---|---|---|---|---|---|---|---|
|
2 |
10.49 |
10.96 |
11.55 |
12.34 |
13.36 |
14.38 |
15.5 |
|
2.5 |
11.27 |
11.77 |
12.55 |
13.52 |
14.61 |
15.71 |
16.61 |
|
3 |
12.05 |
12.58 |
13.12 (13.52) |
14.62 |
15.78 |
16.95 |
17.77 |
|
3.5 |
12.84 |
13.41 |
14.46 |
15.68 |
16.9 |
18.15 |
18.98 |
|
4 |
13.64 |
14.24 |
15.39 |
16.69 |
17.99 |
19.32 |
20.27 |
|
4.5 |
14.45 |
15.1 |
16.3 |
17.69 |
19.06 |
20.5 |
21.63 |
|
5 |
15.27 |
15.96 |
17.22 |
18.67 |
20.14 |
21.7 |
23.09 |
|
5.5 |
16.09 |
16.83 |
18.14 |
19.67 |
21.25 |
22.96 |
24.66 |
|
6 |
16.93 |
17.72 |
19.07 |
20.69 |
22.4 |
24.31 |
26.34 |
|
6.5 |
17.78 |
18.62 |
20.02 |
21.74 |
23.62 |
25.76 |
28.16 |
|
7 |
18.64 |
19.53 |
21 |
22.85 |
24.94 |
27.36 |
30.12 |
|
7.5 |
19.52 |
20.45 |
22.02 |
24.03 |
26.36 |
29.11 |
32.73 |
|
8 |
20.4 |
21.39 |
22.09 (23.18) |
25.3 |
27.91 |
31.06 |
34.51 |
|
8.5 |
21.31 |
22.34 |
24.21 |
26.66 |
29.61 |
33.22 |
36.96 |
|
9 |
22.25 |
23.33 |
25.4 |
28.13 |
31.46 |
35.57 |
39.58 |
|
9.5 |
23.25 |
24.38 |
26.88 |
29.73 |
33.46 |
38.11 |
42.35 |
|
10 |
24.33 |
25.52 |
28.07 |
31.44 |
35.61 |
40.8 |
45.27 |
|
10.5 |
25.51 |
26.78 |
29.59 |
33.3 |
37.92 |
43.63 |
48.31 |
|
11 |
26.8 |
28.17 |
31.25 |
35.3 |
40.38 |
46.57 |
51.47 |
|
11.5 |
28.24 |
29.72 |
33.08 |
37.46 |
43 |
49.61 |
54.73 |
|
12 |
29.85 |
31.46 |
35.09 |
39.78 |
45.77 |
52.73 |
58.09 |
|
12.5 |
31.64 |
33.41 |
37.31 |
42.27 |
48.7 |
55.91 |
61.52 |
|
13 |
33.64 |
35.6 |
39.74 |
44.95 |
51.79 |
59.12 |
65.02 |
|
13.5 |
35.85 |
38.03 |
42.4 |
47.81 |
55.02 |
62.35 |
68.51 |
|
14 |
38.22 |
40.64 |
45.21 |
50.77 |
58.31 |
65.57 |
72.13 |
|
14.5 |
40.66 |
43.34 |
48.08 |
53.76 |
61.58 |
68.76 |
75.66 |
|
15 |
43.11 |
46.06 |
50.92 |
56.71 |
64.72 |
71.91 |
79.12 |
|
15.5 |
45.5 |
48.69 |
53.64 |
59.51 |
67.64 |
74.98 |
82.45 |
|
16 |
47.74 |
51.16 |
56.16 |
62.1 |
70.26 |
77.97 |
85.62 |
|
16.5 |
49.76 |
53.39 |
58.38 |
64.39 |
72.46 |
80.84 |
88.59 |
|
17 |
51.5 |
55.28 |
60.22 |
66.31 |
74.17 |
83.58 |
91.31 |
|
17.5 |
52.89 |
56.78 |
61.61 |
67.78 |
75.32 |
86.14 |
93.73 |
|
18 |
53.97 |
57.89 |
62.61 |
68.88 |
76 |
88.41 |
95.76 |
where:
• In the original table in Nelson the 25th% value at 3 years is given as 13.12. When the data is plotted this value is out of line with others. If the value in pounds is converted to kilograms, the value in parentheses is given. This value is in line with other values.
• Ditto for the 25th% value at 8 years.
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for body weight in kilograms =
= ((-0.00031 * ((years)^5)) + (0.0136338 * ((years)^4)) - (0.209761 * ((years)^3)) + (1.4531328 * ((years)^2)) - (2.881238 * (years)) + 12.09451))
10th% for body weight in kilograms =
= ((-0.00036 * ((years)^5)) + (0.015911 * ((years)^4)) - (0.246219 * ((years)^3)) + (1.715741 * ((years)^2)) - (3.640113 * (years)) + 13.322558))
25th% for body weight in kilograms =
= ((-0.000302 * ((years)^5)) + (0.0124874 * ((years)^4)) - (0.175549 * ((years)^3)) + (1.0989685 * ((years)^2)) - (1.202455 * (years)) + 10.849569))
50th% for body weight in kilograms =
= ((-0.000226 * ((years)^5)) + (0.0085339 * ((years)^4)) - (0.102293 * ((years)^3)) + (0.5277631 * ((years)^2)) + (0.8834021 * (years)) + 9.2603661))
75th% for body weight in kilograms =
= ((-0.000199 * ((years)^5)) + (0.0065687 * ((years)^4)) - (0.059912 * ((years)^3)) + (0.2054266 * ((years)^2)) + (2.0114597 * (years)) + 8.9724996))
90th% for body weight in kilograms =
= ((0.0001102 * ((years)^5)) - (0.007418 * ((years)^4)) + (0.1665908 * ((years)^3)) - (1.361447 * ((years)^2)) + (6.8756582 * (years)) + 4.7534902))
95th% for body weight in kilograms =
= ((-0.000039 * ((years)^5)) + (0.0001188 * ((years)^4)) + (0.0226668 * ((years)^3)) - (0.082857 * ((years)^2)) + (2.2409441 * (years)) + 11.173896))
Distribution of Weight 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.
Age 2-18 years, 5 to 50%ile
|
Age in years |
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
2 |
7.8171662 |
-153.7805 |
757.59112 |
|
2.5 |
4.8016831 |
-98.85943 |
508.98526 |
|
3 |
3.6364200 |
-79.4059 |
433.69354 |
|
3.5 |
2.9181603 |
-67.33574 |
388.39055 |
|
4 |
2.5703089 |
-63.1911 |
388.69352 |
|
4.5 |
2.2502849 |
-58.39822 |
378.8992 |
|
5 |
2.0866071 |
-57.55004 |
397.1625 |
|
5.5 |
1.8835059 |
-57.55004 |
397.96257 |
|
6 |
1.6799713 |
-51.16471 |
389.50855 |
|
6.5 |
1.4861965 |
-47.29001 |
375.75047 |
|
7 |
1.2687619 |
-41.86359 |
344.22888 |
|
7.5 |
1.0457138 |
-35.47738 |
298.77775 |
|
8 |
0.9624000 |
-34.76181 |
313.48255 |
|
8.5 |
0.6538694 |
-22.8873 |
195.5138 |
|
9 |
0.5011416 |
-17.54015 |
146.91839 |
|
9.5 |
0.4987187 |
-19.49062 |
188.63448 |
|
10 |
0.2994737 |
-10.34415 |
79.234954 |
|
10.5 |
0.2409577 |
-8.373125 |
61.658324 |
|
11 |
0.2010660 |
-7.175789 |
52.783221 |
|
11.5 |
0.1733817 |
-6.498118 |
50.141261 |
|
12 |
0.1545501 |
-6.218652 |
52.829694 |
|
12.5 |
0.1443470 |
-6.424955 |
63.691006 |
|
13 |
0.1368635 |
-6.764871 |
77.575624 |
|
13.5 |
0.1340544 |
-7.438398 |
99.244528 |
|
14 |
0.1338386 |
-8.30911 |
126.91713 |
|
14.5 |
0.1344463 |
-9.242213 |
158.34938 |
|
15 |
0.1344312 |
-10.09039 |
189.96474 |
|
15.5 |
0.1346655 |
-10.90781 |
222.30127 |
|
16 |
0.1347465 |
-11.64316 |
253.50712 |
|
16.5 |
0.1343701 |
-12.235 |
280.83247 |
|
17 |
0.1327343 |
-12.56691 |
299.83322 |
|
17.5 |
0.1309002 |
-12.73545 |
312.02546 |
|
18 |
0.1270691 |
-12.54842 |
311.67768 |
Age 2-18 years, 51 to 95%ile
|
Age in years |
wgt^3 |
wgt^2 |
wgt |
coefficient |
|---|---|---|---|---|
|
2 |
|
-4.795264 |
147.73931 |
-1042.899 |
|
2.5 |
|
-4.15549 |
139.75247 |
-1079.849 |
|
3 |
|
-3.602617 |
130.94463 |
-1094.336 |
|
3.5 |
|
-3.223541 |
125.31533 |
-1122.338 |
|
4 |
|
-2.868675 |
118.5605 |
-1129.638 |
|
4.5 |
|
-2.586558 |
113.07919 |
-1140.866 |
|
5 |
|
-2.246622 |
103.95714 |
-1107.687 |
|
5.5 |
0.0868 |
-7.689 |
221.3746 |
-1990.216 |
|
6 |
0.088687 |
-7.8467 |
229.1679 |
-2117.982 |
|
6.5 |
0.074655 |
-6.87377 |
209.82268 |
-2029.884 |
|
7 |
0.05929 |
-5.7336 |
184.347 |
-1876.041 |
|
7.5 |
0.0458556 |
-4.683922 |
159.364 |
-1711.127 |
|
8 |
0.036298 |
-3.895 |
139.69559 |
-1578.917 |
|
8.5 |
0.0267 |
-3.04793 |
116.5156 |
-1395.924 |
|
9 |
0.0194433 |
-2.368756 |
96.825857 |
-1232.114 |
|
9.5 |
0.01463 |
-1.8971 |
82.710947 |
-1116.68 |
|
10 |
0.0107258 |
-1.488513 |
69.588334 |
-999.8339 |
|
10.5 |
0.007963 |
-1.184086 |
59.406344 |
-909.2527 |
|
11 |
0.0058845 |
-0.941 |
50.82315 |
-830.2874 |
|
11.5 |
0.0043098 |
-0.745217 |
43.513949 |
-760.8555 |
|
12 |
0.0030939 |
-0.583689 |
37.097746 |
-696.85 |
|
12.5 |
0.0020655 |
-0.435902 |
30.7 |
-624.8732 |
|
13 |
0.0011409 |
-0.2913 |
23.81836 |
-535.5889 |
|
13.5 |
|
-0.094929 |
13.212988 |
-364.695 |
|
14 |
|
-0.088972 |
13.046236 |
-383.0703 |
|
14.5 |
|
-0.084523 |
13.004695 |
-404.9573 |
|
15 |
|
-0.081512 |
13.09326 |
-430.5118 |
|
15.5 |
|
-0.079081 |
13.200439 |
-455.6319 |
|
16 |
|
-0.077023 |
13.298006 |
-478.8528 |
|
16.5 |
|
-0.075347 |
13.381186 |
-499.1644 |
|
17 |
0.00146 |
-0.41996 |
40.481199 |
-1214.671 |
|
17.5 |
0.0025265 |
-0.684265 |
62.395055 |
-1822.273 |
|
18 |
0.0033912 |
-0.909 |
81.7816 |
-2378.522 |
