The distribution of weight for a given height in boys from age 4 years to prepuberty can be used to evaluate the physical development of a child.
Data: height in centimeters and weight in kilograms.
|
length |
5th% |
10th% |
25th% |
50th% |
75th% |
90th% |
95th% |
|---|---|---|---|---|---|---|---|
|
90 |
11.7 |
11.97 |
12.59 |
13.41 |
14.35 |
15.25 |
15.72 |
|
92 |
12.07 |
12.36 |
13.03 |
13.89 |
14.84 |
15.87 |
16.41 |
|
94 |
12.46 |
12.77 |
13.49 |
14.38 |
15.34 |
16.45 |
17.06 |
|
96 |
12.87 |
13.21 |
13.98 |
14.89 |
15.87 |
17.01 |
17.69 |
|
98 |
13.31 |
13.67 |
14.48 |
15.43 |
16.41 |
17.56 |
18.29 |
|
100 |
13.77 |
14.15 |
15 |
15.98 |
16.98 |
18.11 |
18.89 |
|
102 |
14.25 |
14.65 |
15.54 |
16.65 |
17.57 |
18.67 |
19.5 |
|
104 |
14.76 |
15.18 |
16.1 |
17.13 |
18.18 |
19.25 |
20.12 |
|
106 |
15.3 |
15.73 |
16.68 |
17.74 |
18.82 |
19.86 |
20.76 |
|
108 |
15.85 |
16.31 |
17.28 |
18.37 |
19.49 |
20.51 |
21.45 |
|
110 |
16.43 |
16.91 |
17.9 |
19.02 |
20.18 |
21.22 |
22.18 |
|
112 |
17.04 |
17.53 |
18.54 |
19.7 |
20.91 |
21.98 |
22.98 |
|
114 |
17.66 |
18.18 |
19.2 |
20.39 |
21.66 |
22.82 |
23.85 |
|
116 |
18.32 |
18.85 |
19.89 |
21.11 |
22.45 |
23.73 |
24.8 |
|
118 |
18.99 |
19.55 |
20.6 |
21.85 |
23.28 |
24.73 |
25.83 |
|
120 |
19.7 |
20.28 |
21.34 |
22.63 |
24.15 |
25.8 |
26.96 |
|
122 |
20.43 |
21.03 |
22.11 |
23.45 |
25.07 |
26.96 |
28.18 |
|
124 |
21.2 |
21.82 |
22.92 |
24.32 |
26.05 |
28.18 |
29.5 |
|
126 |
21.99 |
22.64 |
23.77 |
25.24 |
27.1 |
29.48 |
30.92 |
|
128 |
22.82 |
23.5 |
24.67 |
26.22 |
28.21 |
30.86 |
32.44 |
|
130 |
23.69 |
24.59 |
25.62 |
27.26 |
29.41 |
32.31 |
34.07 |
|
132 |
24.59 |
25.32 |
26.62 |
28.38 |
30.68 |
33.82 |
35.81 |
|
134 |
25.53 |
26.3 |
27.68 |
29.58 |
32.05 |
35.4 |
37.67 |
|
136 |
26.51 |
27.32 |
28.8 |
30.86 |
33.51 |
37.05 |
39.65 |
|
138 |
27.53 |
28.38 |
29.99 |
32.23 |
35.08 |
38.77 |
41.74 |
|
140 |
28.59 |
29.48 |
31.25 |
33.7 |
36.75 |
40.55 |
43.97 |
|
142 |
29.7 |
30.64 |
32.58 |
35.27 |
38.54 |
42.39 |
46.32 |
|
144 |
30.86 |
31.85 |
34 |
36.95 |
40.45 |
44.29 |
48.8 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0000206 * ((height in cm)^3)) - (0.003651 * ((height in cm)^2)) + (0.3468137 * (height in cm)) - 5.0122)
10th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0000224 * ((height in cm)^3)) - (0.004153 * ((height in cm)^2)) + (0.4054487 * (height in cm)) - 7.20508)
25th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0000546 * ((height in cm)^3)) - (0.01503 * ((height in cm)^2)) + (1.6297267 * (height in cm)) - 52.26795)
50th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0000845 * ((height in cm)^3)) - (0.024617 * ((height in cm)^2)) + (2.6668046 * (height in cm)) - 88.89839)
75th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0000927 * ((height in cm)^3)) - (0.026355 * ((height in cm)^2)) + (2.7760025 * (height in cm)) - 89.70869)
90th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0000625 * ((height in cm)^3)) - (0.01422 * ((height in cm)^2)) + (1.2514278 * (height in cm)) - 27.51365)
95th% of weight in kilograms for height in centimeters from 90 - 144 cm =
= ((0.0001348 * ((height in cm)^3)) - (0.037719 * ((height in cm)^2)) + (3.8023707 * (height in cm)) - 119.1073)
Distribution of Weight for Height
If the same data is analyzed for each month, then the percentile represented by a weight for 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.
>= 4 years, 5 to 50%ile
|
|
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
90 |
4.7616242 |
-93.17752 |
443.25724 |
|
92 |
4.5643645 |
-93.72716 |
471.27004 |
|
94 |
4.5194200 |
-97.86120 |
522.69936 |
|
96 |
4.6579131 |
-107.04760 |
611.21403 |
|
98 |
4.3257605 |
-103.11910 |
611.22021 |
|
100 |
4.1508798 |
-103.16030 |
638.51260 |
|
102 |
2.9490407 |
-72.34683 |
437.04720 |
|
104 |
3.8959873 |
-105.30160 |
710.56608 |
|
106 |
3.6755169 |
-103.04730 |
721.31946 |
|
108 |
3.5252991 |
-102.80380 |
748.85545 |
|
110 |
3.3537550 |
-101.52710 |
767.78404 |
|
112 |
3.0902887 |
-96.61924 |
754.08935 |
|
114 |
2.9684629 |
-96.43727 |
782.22979 |
|
116 |
2.8112757 |
-94.68728 |
796.07472 |
|
118 |
2.7077679 |
-94.79488 |
828.55711 |
|
120 |
2.5313893 |
-91.71848 |
829.27567 |
|
122 |
2.3270491 |
-87.11934 |
813.36340 |
|
124 |
2.0999665 |
-81.06063 |
779.42111 |
|
126 |
1.8881228 |
-75.21015 |
745.55161 |
|
128 |
1.6772682 |
-68.89175 |
703.33795 |
|
130 |
1.7303284 |
-75.28390 |
816.69411 |
|
132 |
1.2331691 |
-53.33337 |
570.46998 |
|
134 |
1.0274721 |
-45.40099 |
494.04271 |
|
136 |
0.8442835 |
-37.98812 |
418.36025 |
|
138 |
0.6905776 |
-31.60651 |
351.40523 |
|
140 |
0.5558935 |
-25.75114 |
286.55674 |
|
142 |
0.4428702 |
-20.63781 |
227.03310 |
|
144 |
0.3579950 |
-16.84699 |
183.76610 |
>= 4 years, 51 to 95%ile
|
|
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
90 |
-5.1087210 |
168.238390 |
-1287.3480 |
|
92 |
-5.1149690 |
172.659820 |
-1361.2620 |
|
94 |
-5.0060500 |
173.949930 |
-1416.0130 |
|
96 |
-4.8201080 |
172.896890 |
-1455.5350 |
|
98 |
-4.8177580 |
177.978930 |
-1548.9410 |
|
100 |
-4.7010400 |
179.236010 |
-1613.5490 |
|
102 |
-5.4139010 |
211.285590 |
-1966.7640 |
|
104 |
-4.4615730 |
181.217650 |
-1745.0340 |
|
106 |
-4.3180670 |
181.178240 |
-1805.2150 |
|
108 |
-4.1095860 |
178.337230 |
-1839.3580 |
|
110 |
-3.8468790 |
172.825730 |
-1845.6240 |
|
112 |
-3.5535640 |
165.487000 |
-1831.1340 |
|
114 |
-3.1766960 |
153.612970 |
-1761.5530 |
|
116 |
-2.7992240 |
140.737850 |
-1673.5990 |
|
118 |
-2.3929070 |
125.379870 |
-1547.0900 |
|
120 |
-2.0638860 |
112.668870 |
-1442.6200 |
|
122 |
-1.7673800 |
100.642000 |
-1337.9380 |
|
124 |
-1.5178610 |
90.228705 |
-1246.2900 |
|
126 |
-1.2921460 |
80.326740 |
-1153.8960 |
|
128 |
-1.1080770 |
72.060909 |
-1077.1930 |
|
130 |
-0.9414860 |
64.184154 |
-999.5508 |
|
132 |
-0.8135500 |
58.122097 |
-943.7303 |
|
134 |
-0.7030910 |
52.706920 |
-893.3562 |
|
136 |
-0.6111030 |
48.089456 |
-851.5479 |
|
138 |
-0.5338470 |
44.124865 |
-817.1300 |
|
140 |
-0.4723660 |
40.996831 |
-794.7226 |
|
142 |
-0.4213010 |
38.396802 |
-779.8574 |
|
144 |
-0.3800810 |
36.362910 |
-774.4967 |
