The distribution of weight for a given height in girls 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 |
11.45 |
11.67 |
12.28 |
13.14 |
14.11 |
14.98 |
15.74 |
|
92 |
11.86 |
12.1 |
12.74 |
13.63 |
14.63 |
15.57 |
16.42 |
|
94 |
12.26 |
12.53 |
13.21 |
14.12 |
15.14 |
16.13 |
17.05 |
|
96 |
12.66 |
12.97 |
13.7 |
14.62 |
15.66 |
16.69 |
17.65 |
|
98 |
13.06 |
13.42 |
14.19 |
15.13 |
16.19 |
17.24 |
18.23 |
|
100 |
13.48 |
13.88 |
14.69 |
15.65 |
16.73 |
17.8 |
18.8 |
|
102 |
13.91 |
14.36 |
15.21 |
16.2 |
17.28 |
18.38 |
19.38 |
|
104 |
14.36 |
14.85 |
15.75 |
16.75 |
17.86 |
18.98 |
19.98 |
|
106 |
14.84 |
15.37 |
16.3 |
17.33 |
18.46 |
19.62 |
20.61 |
|
108 |
15.35 |
15.91 |
16.87 |
17.94 |
19.09 |
20.3 |
21.29 |
|
110 |
15.9 |
16.48 |
17.47 |
18.56 |
19.76 |
21.03 |
22.03 |
|
112 |
16.48 |
17.09 |
18.08 |
19.22 |
20.47 |
21.81 |
22.84 |
|
114 |
17.11 |
17.72 |
18.72 |
19.91 |
21.23 |
22.67 |
23.73 |
|
116 |
17.77 |
18.4 |
19.4 |
20.64 |
22.04 |
23.6 |
24.71 |
|
118 |
18.48 |
19.11 |
20.11 |
21.42 |
22.92 |
24.62 |
25.81 |
|
120 |
19.22 |
19.85 |
20.87 |
22.25 |
23.88 |
25.73 |
27.03 |
|
122 |
19.99 |
20.64 |
21.68 |
23.13 |
24.91 |
26.95 |
28.37 |
|
124 |
20.8 |
21.47 |
22.54 |
24.09 |
26.05 |
28.27 |
29.87 |
|
126 |
21.65 |
22.34 |
23.47 |
25.11 |
27.28 |
29.71 |
31.51 |
|
128 |
22.53 |
23.25 |
24.46 |
26.22 |
28.63 |
31.28 |
33.33 |
|
130 |
23.44 |
24.22 |
25.52 |
27.4 |
30.09 |
32.99 |
35.33 |
|
132 |
24.38 |
25.22 |
26.66 |
28.68 |
31.68 |
34.84 |
37.53 |
|
134 |
25.35 |
26.28 |
27.88 |
30.06 |
33.41 |
36.84 |
39.93 |
|
136 |
26.34 |
27.39 |
29.19 |
31.54 |
35.29 |
39.01 |
42.54 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.0000247 * ((height in cm)^3)) - (0.004347 * ((height in cm)^2)) + (0.3462385 * (height in cm)) - 2.430703)
10th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.000045 * ((height in cm)^3)) - (0.011234 * ((height in cm)^2)) + (1.1314881 * (height in cm)) - 31.97981)
25th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.0000848 * ((height in cm)^3)) - (0.02435 * ((height in cm)^2)) + (2.5783033 * (height in cm)) - 84.39121)
50th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.0001012 * ((height in cm)^3)) - (0.029076 * ((height in cm)^2)) + (3.04138 * (height in cm)) - 98.88346)
75th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.0001522 * ((height in cm)^3)) - (0.044326 * ((height in cm)^2)) + (4.5682013 * (height in cm)) - 148.9818)
90th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.0001785 * ((height in cm)^3)) - (0.051505 * ((height in cm)^2)) + (5.2305385 * (height in cm)) - 168.692)
95th% of weight in kilograms for height in centimeters from 90 - 136 cm =
= ((0.0002599 * ((height in cm)^3)) - (0.077011 * ((height in cm)^2)) + (7.8924149 * (height in cm)) - 260.2659)
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 |
2.9288203 |
-45.41748 |
141.09140 |
|
92 |
3.0280147 |
-51.76310 |
192.99520 |
|
94 |
3.4605960 |
-67.08499 |
307.28922 |
|
96 |
4.0617337 |
-87.83507 |
465.97933 |
|
98 |
4.3386455 |
-100.53060 |
577.85349 |
|
100 |
4.4279428 |
-108.21210 |
659.03482 |
|
102 |
4.3727600 |
-111.96470 |
716.26756 |
|
104 |
4.4613147 |
-119.94760 |
807.45428 |
|
106 |
4.2838279 |
-119.71210 |
838.07092 |
|
108 |
3.9935310 |
-115.53260 |
837.38985 |
|
110 |
3.8715719 |
-116.46970 |
878.04442 |
|
112 |
3.5470193 |
-110.12950 |
856.44950 |
|
114 |
3.1917465 |
-101.99080 |
815.47671 |
|
116 |
2.9167451 |
-96.22230 |
793.56786 |
|
118 |
2.5100425 |
-84.68278 |
712.37704 |
|
120 |
2.1630207 |
-74.67894 |
640.89894 |
|
122 |
1.9113350 |
-67.90295 |
598.17072 |
|
124 |
1.5929739 |
-57.63830 |
514.20033 |
|
126 |
1.3845571 |
-51.55847 |
471.78630 |
|
128 |
1.1669840 |
-44.53416 |
415.52251 |
|
130 |
1.0412208 |
-41.42204 |
403.38378 |
|
132 |
0.9200178 |
-38.22933 |
389.77609 |
|
134 |
0.8198029 |
-35.77032 |
384.58445 |
|
136 |
0.7431815 |
-34.28314 |
392.09002 |
|
138 |
|
|
|
|
140 |
|
|
|
|
142 |
|
|
|
|
144 |
|
|
|
>= 4 years, 51 to 95%ile
|
|
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
90 |
-5.450236 |
174.820510 |
-1306.2230 |
|
92 |
-5.097557 |
169.371430 |
-1311.5990 |
|
94 |
-4.858160 |
166.815870 |
-1336.8860 |
|
96 |
-4.636192 |
164.469950 |
-1363.6030 |
|
98 |
-4.464659 |
163.465610 |
-1401.2110 |
|
100 |
-4.298985 |
162.393700 |
-1438.5550 |
|
102 |
-4.243756 |
165.125060 |
-1511.2660 |
|
104 |
-4.030757 |
161.971290 |
-1532.1250 |
|
106 |
-3.854043 |
159.914120 |
-1563.7900 |
|
108 |
-3.677700 |
157.657080 |
-1594.6470 |
|
110 |
-3.363668 |
149.441970 |
-1564.8610 |
|
112 |
-3.081426 |
141.967830 |
-1540.2120 |
|
114 |
-2.739822 |
131.264180 |
-1477.2500 |
|
116 |
-2.413451 |
120.410570 |
-1406.9580 |
|
118 |
-2.088068 |
108.767310 |
-1321.5680 |
|
120 |
-1.767510 |
96.422041 |
-1220.1720 |
|
122 |
-1.476261 |
84.521731 |
-1114.9870 |
|
124 |
-1.224165 |
73.765217 |
-1016.3990 |
|
126 |
-1.003930 |
63.811970 |
-919.1577 |
|
128 |
-0.820935 |
55.170029 |
-832.0313 |
|
130 |
-0.665159 |
47.368166 |
-748.3993 |
|
132 |
-0.540940 |
40.881099 |
-677.4451 |
|
134 |
-0.439934 |
35.342519 |
-614.8342 |
|
136 |
-0.356586 |
30.508832 |
-557.5376 |
|
138 |
|
|
|
|
140 |
|
|
|
|
142 |
|
|
|
|
144 |
|
|
|
