The distribution of weight for a given height in boys 0-4 years of age 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% |
|---|---|---|---|---|---|---|---|
|
48 |
• |
• |
2.86 |
3.15 |
3.5 |
• |
• |
|
50 |
• |
• |
3.16 |
3.48 |
3.86 |
• |
• |
|
52 |
• |
• |
3.56 |
3.88 |
4.28 |
• |
• |
|
54 |
3.49 |
3.65 |
3.95 |
4.34 |
4.76 |
5.13 |
5.33 |
|
56 |
3.9 |
4.09 |
4.43 |
4.84 |
5.29 |
5.69 |
5.88 |
|
58 |
4.37 |
4.58 |
4.94 |
5.38 |
5.84 |
6.28 |
6.47 |
|
60 |
4.88 |
5.1 |
5.49 |
5.94 |
6.42 |
6.88 |
7.08 |
|
62 |
5.43 |
5.65 |
6.05 |
6.52 |
7.02 |
7.5 |
7.72 |
|
64 |
5.99 |
6.2 |
6.62 |
7.11 |
7.63 |
8.13 |
8.36 |
|
66 |
6.55 |
6.76 |
7.19 |
7.7 |
8.23 |
8.75 |
8.99 |
|
68 |
7.1 |
7.31 |
7.75 |
8.27 |
8.82 |
9.35 |
9.62 |
|
70 |
7.63 |
7.84 |
8.28 |
8.82 |
9.39 |
9.93 |
10.21 |
|
72 |
8.13 |
8.33 |
8.78 |
9.33 |
9.92 |
10.48 |
10.77 |
|
74 |
8.58 |
8.78 |
9.24 |
9.81 |
10.43 |
10.99 |
11.29 |
|
76 |
9 |
9.21 |
9.68 |
10.27 |
10.91 |
11.48 |
11.78 |
|
78 |
9.4 |
9.62 |
10.09 |
10.7 |
11.36 |
11.94 |
12.25 |
|
80 |
9.77 |
10.01 |
10.49 |
11.12 |
11.8 |
12.39 |
12.69 |
|
82 |
10.14 |
10.39 |
10.88 |
11.53 |
12.23 |
12.83 |
13.13 |
|
84 |
10.49 |
10.76 |
11.27 |
11.93 |
12.65 |
13.26 |
13.56 |
|
86 |
10.85 |
11.14 |
11.67 |
12.34 |
13.07 |
13.69 |
14 |
|
88 |
11.22 |
11.53 |
12.08 |
12.76 |
13.5 |
14.13 |
14.44 |
|
90 |
11.6 |
11.94 |
12.52 |
13.2 |
13.94 |
14.58 |
14.9 |
|
92 |
12 |
12.37 |
12.97 |
13.65 |
14.4 |
15.05 |
15.39 |
|
94 |
12.42 |
12.81 |
13.45 |
14.14 |
14.88 |
15.54 |
15.9 |
|
96 |
12.88 |
13.28 |
13.96 |
14.66 |
15.39 |
16.06 |
16.43 |
|
98 |
13.37 |
13.78 |
14.5 |
15.21 |
15.94 |
16.62 |
17 |
|
100 |
13.9 |
14.3 |
15.06 |
15.81 |
16.54 |
17.22 |
17.6 |
|
102 |
14.48 |
14.85 |
15.65 |
16.45 |
17.18 |
17.87 |
18.24 |
Polynomial equations approximating this data were generated in JMP. Because of the nature of the dual curve shown by the data, a single polynomial equation proved to be inaccurate. The data was subdivided about its midpoint and equations calculations made on each side (low end to 78, and 78 to high end).
5th% of weight in kilograms for height in centimeters from 54 - 78 cm =
= ((-0.000222 * ((height in cm)^3)) + (0.0431515 * ((height in cm)^2)) - (2.519557 * (height in cm)) + 48.631069)
5th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.0001191 * ((height in cm)^3)) - (0.029792 * ((height in cm)^2)) + (2.6629158 * (height in cm)) - 73.57287)
10th% of weight in kilograms for height in centimeters from 54 - 78 cm =
= ((-0.000187 * ((height in cm)^3)) + (0.0361482 * ((height in cm)^2)) - (2.049809 * (height in cm)) + 38.40048)
10th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.0000721 * ((height in cm)^3)) - (0.017407 * ((height in cm)^2)) + (1.5882817 * (height in cm)) - 42.57662)
25th% of weight in kilograms for height in centimeters from 48 -78 cm =
= ((-0.000191 * ((height in cm)^3)) + (0.036745 * ((height in cm)^2)) - (2.069121 * (height in cm)) + 38.666782)
25th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.0000692 * ((height in cm)^3)) - (0.016211 * ((height in cm)^2)) + (1.4579987 * (height in cm)) - 37.83925)
50th% of weight in kilograms for height in centimeters from 48 - 78 cm =
= ((-0.000183 * ((height in cm)^3)) + (0.0350707 * ((height in cm)^2)) - (1.94444 * (height in cm)) + 35.935034)
50th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.0001155 * ((height in cm)^3)) - (0.028535 * ((height in cm)^2)) + (2.5535985 * (height in cm)) - 69.66125)
75th% of weight in kilograms for height in centimeters from 48 -78 cm =
= ((-0.000176 * ((height in cm)^3)) + (0.0336892 * ((height in cm)^2)) - (1.848631 * (height in cm)) + 34.062209)
75th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.00013 * ((height in cm)^3)) - (0.032809 * ((height in cm)^2)) + (2.9698614 * (height in cm)) - 82.38166)
90th% of weight in kilograms for height in centimeters from 54 -78 cm =
= ((-0.000147 * ((height in cm)^3)) + (0.0276499 * ((height in cm)^2)) - (1.422264 * (height in cm)) + 24.469411)
90th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.000126 * ((height in cm)^3)) - (0.031769 * ((height in cm)^2)) + (2.8850216 * (height in cm)) - 79.61287)
95th% of weight in kilograms for height in centimeters from 54 -78 cm =
= ((-0.000174 * ((height in cm)^3)) + (0.0330935 * ((height in cm)^2)) - (1.775404 * (height in cm)) + 32.163387)
95th% of weight in kilograms for height in centimeters from 78 - 102 cm =
= ((0.0000951 * ((height in cm)^3)) - (0.023308 * ((height in cm)^2)) + (2.1212925 * (height in cm)) - 56.51545)
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
|
<= 4 years old |
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
54 |
25.4484280 |
-145.9461 |
204.13808 |
|
56 |
25.5306510 |
-175.0249 |
299.10546 |
|
58 |
22.4533020 |
-174.0803 |
336.72752 |
|
60 |
21.9145600 |
-194.5251 |
432.29840 |
|
62 |
19.6355760 |
-193.2123 |
475.06830 |
|
64 |
17.3430450 |
-186.9605 |
502.57589 |
|
66 |
15.5872100 |
-182.9269 |
534.38633 |
|
68 |
14.8649400 |
-189.9787 |
604.47578 |
|
70 |
13.2272180 |
-179.6826 |
605.84540 |
|
72 |
12.2702770 |
-176.7203 |
630.69061 |
|
74 |
11.0476180 |
-166.5640 |
620.81674 |
|
76 |
10.2964920 |
-162.9234 |
637.23583 |
|
78 |
9.4524986 |
-155.2432 |
628.91873 |
|
80 |
9.1665082 |
-157.9570 |
673.05520 |
|
82 |
8.6105740 |
-153.9973 |
680.95255 |
|
84 |
8.8890176 |
-167.8313 |
787.16423 |
|
86 |
9.0577962 |
-179.6514 |
887.68409 |
|
88 |
9.1407059 |
-189.7911 |
983.53405 |
|
90 |
9.6760472 |
-211.7103 |
1158.67720 |
|
92 |
10.0323530 |
-229.9521 |
1319.64350 |
|
94 |
9.8443389 |
-235.2730 |
1408.50750 |
|
96 |
9.5531300 |
-237.8604 |
1483.88970 |
|
98 |
9.2620090 |
-240.3701 |
1563.24980 |
|
100 |
8.1613700 |
-219.0556 |
1473.20670 |
|
102 |
6.9309249 |
-191.7044 |
1327.92570 |
< 4 years, 51 to 95%ile
|
|
wgt^2 |
wgt |
coefficient |
|---|---|---|---|
|
54 |
-24.932410 |
286.62827 |
-724.3695 |
|
56 |
-20.679680 |
264.89794 |
-747.6587 |
|
58 |
-20.107630 |
279.27973 |
-870.4537 |
|
60 |
-18.528250 |
280.44599 |
-962.0373 |
|
62 |
-17.374550 |
284.70018 |
-1067.5850 |
|
64 |
-16.095110 |
284.78622 |
-1161.1270 |
|
66 |
-15.659460 |
296.00823 |
-1300.7400 |
|
68 |
-14.848090 |
298.83829 |
-1405.8430 |
|
70 |
-13.809130 |
295.07699 |
-1478.3030 |
|
72 |
-12.893140 |
290.31649 |
-1536.2870 |
|
74 |
-11.555050 |
274.22759 |
-1528.1640 |
|
76 |
-10.687040 |
265.47112 |
-1549.2030 |
|
78 |
-10.033860 |
259.35597 |
-1576.3500 |
|
80 |
-9.165458 |
246.92599 |
-1562.4800 |
|
82 |
-8.498092 |
237.72633 |
-1561.2550 |
|
84 |
-7.885094 |
228.63981 |
-1555.4430 |
|
86 |
-7.752908 |
231.36761 |
-1624.5150 |
|
88 |
-7.499759 |
230.81416 |
-1674.1090 |
|
90 |
-7.659927 |
241.74041 |
-1806.3180 |
|
92 |
-7.626960 |
247.39583 |
-1905.8990 |
|
94 |
-8.115899 |
269.40273 |
-2136.6800 |
|
96 |
-8.488894 |
289.34622 |
-2367.4210 |
|
98 |
-8.569350 |
301.14732 |
-2547.9770 |
|
100 |
-8.569350 |
311.43054 |
-2731.7500 |
|
102 |
-8.500693 |
319.98090 |
-2913.3540 |
