The distribution of weight for girls 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 |
9.95 |
10.32 |
10.96 |
11.8 |
12.73 |
13.58 |
14.15 |
|
2.5 |
10.8 |
11.35 |
12.11 |
13.03 |
14.23 |
15.16 |
15.76 |
|
3 |
11.61 |
12.26 |
13.11 |
14.1 |
15.5 |
16.54 |
17.22 |
|
3.5 |
12.37 |
13.08 |
14 |
15.07 |
16.59 |
17.77 |
18.59 |
|
4 |
13.11 |
13.84 |
14.8 |
15.96 |
17.56 |
18.93 |
19.91 |
|
4.5 |
13.83 |
14.56 |
15.55 |
16.81 |
18.48 |
20.06 |
21.24 |
|
5 |
14.55 |
15.26 |
16.29 |
17.66 |
19.39 |
21.23 |
22.62 |
|
5.5 |
15.29 |
15.97 |
17.05 |
18.56 |
20.36 |
22.48 |
24.11 |
|
6 |
16.05 |
16.72 |
17.86 |
19.52 |
21.44 |
23.89 |
25.75 |
|
6.5 |
16.85 |
17.51 |
18.76 |
20.61 |
22.68 |
25.5 |
27.59 |
|
7 |
17.71 |
18.39 |
19.78 |
21.84 |
24.16 |
27.39 |
29.68 |
|
7.5 |
18.62 |
19.37 |
20.95 |
23.26 |
25.9 |
29.57 |
32.07 |
|
8 |
19.62 |
20.45 |
22.26 |
24.84 |
27.88 |
32.04 |
34.71 |
|
8.5 |
20.68 |
21.64 |
23.7 |
26.58 |
30.08 |
34.73 |
37.58 |
|
9 |
21.82 |
22.92 |
25.27 |
28.46 |
32.44 |
37.6 |
40.64 |
|
9.5 |
23.05 |
24.29 |
26.94 |
30.45 |
34.94 |
40.61 |
43.85 |
|
10 |
24.36 |
25.76 |
28.71 |
32.55 |
37.53 |
43.7 |
47.17 |
|
10.5 |
25.75 |
27.32 |
30.57 |
34.72 |
40.17 |
46.84 |
50.57 |
|
11 |
27.24 |
28.97 |
32.49 |
36.95 |
42.84 |
49.96 |
54 |
|
11.5 |
28.83 |
30.71 |
34.48 |
39.23 |
45.48 |
53.03 |
57.42 |
|
12 |
30.52 |
32.53 |
36.52 |
41.53 |
48.07 |
55.99 |
60.81 |
|
12.5 |
32.3 |
34.42 |
38.59 |
43.84 |
50.56 |
58.81 |
64.12 |
|
13 |
34.14 |
36.35 |
40.55 |
46.1 |
52.91 |
61.45 |
67.3 |
|
13.5 |
35.98 |
38.26 |
42.65 |
48.26 |
55.11 |
63.87 |
70.3 |
|
14 |
37.76 |
40.11 |
44.54 |
50.28 |
57.09 |
66.04 |
73.08 |
|
14.5 |
39.45 |
41.83 |
46.28 |
52.1 |
58.84 |
67.95 |
75.59 |
|
15 |
40.99 |
43.38 |
47.82 |
53.68 |
60.32 |
69.54 |
77.78 |
|
15.5 |
42.32 |
44.72 |
49.1 |
54.96 |
61.48 |
70.79 |
79.59 |
|
16 |
43.41 |
45.78 |
50.09 |
55.89 |
62.29 |
71.68 |
80.99 |
|
16.5 |
44.2 |
46.54 |
50.75 |
56.44 |
62.75 |
72.18 |
81.93 |
|
17 |
44.74 |
47.04 |
51.14 |
56.69 |
62.91 |
72.38 |
82.46 |
|
17.5 |
45.08 |
47.33 |
51.33 |
56.71 |
62.89 |
72.37 |
82.62 |
|
18 |
45.26 |
47.47 |
51.39 |
56.62 |
62.78 |
72.25 |
82.47 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for body weight in kilograms =
= ((-0.002176 * ((years)^4)) + (0.07685 * ((years)^3)) - (0.813337 * ((years)^2)) + (4.7825778 * (years)) + 2.8002366))
10th% for body weight in kilograms =
= ((-0.002375 * ((years)^4)) + (0.0824921 * ((years)^3)) - (0.851709 * ((years)^2)) + (4.8946818 * (years)) + 3.2497516))
25th% for body weight in kilograms =
= ((0.0000876 * ((years)^5)) - (0.006799 * ((years)^4)) + (0.1606151 * ((years)^3)) - (1.422992 * ((years)^2)) + (6.7780349 * (years)) + 1.8403147))
50th% for body weight in kilograms =
= ((0.0001374 * ((years)^5)) - (0.009388 * ((years)^4)) + (0.2054083 * ((years)^3)) - (1.718213 * ((years)^2)) + (7.7507354 * (years)) + 1.5783902))
75th% for body weight in kilograms =
= ((0.000329 * ((years)^5)) - (0.018742 * ((years)^4)) + (0.3665432 * ((years)^3)) - (2.891519 * ((years)^2)) + (11.629457 * (years)) - 1.712358))
90th% for body weight in kilograms =
= ((0.0003912 * ((years)^5)) - (0.021602 * ((years)^4)) + (0.408011 * ((years)^3)) - (3.073118 * ((years)^2)) + (12.121782 * (years)) - 1.40964))
95th% for body weight in kilograms =
= ((0.0002603 * ((years)^5)) - (0.015664 * ((years)^4)) + (0.3110804 * ((years)^3)) - (2.349683 * ((years)^2)) + (10.047066 * (years)) + 1.1249541))
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.
2 to 18 years, 5 to 50%ile
|
Age in years |
wgt^2 |
wgt |
constant |
|---|---|---|---|
|
2 |
5.7479630 |
-100.47290 |
435.32884 |
|
2.5 |
5.7143085 |
-115.80870 |
588.93702 |
|
3 |
5.0709912 |
-112.16210 |
623.44431 |
|
3.5 |
4.3540292 |
-102.67790 |
608.65872 |
|
4 |
3.6661269 |
-90.63418 |
562.82326 |
|
4.5 |
3.0189875 |
-77.22619 |
495.2386 |
|
5 |
2.4016316 |
-62.70540 |
408.52137 |
|
5.5 |
1.7673233 |
-45.88391 |
292.94598 |
|
6 |
1.2926113 |
-32.84130 |
198.65911 |
|
6.5 |
0.8893096 |
-21.21277 |
109.53115 |
|
7 |
0.6461516 |
-14.55918 |
59.83594 |
|
7.5 |
0.5135676 |
-11.73215 |
45.094219 |
|
8 |
0.4237503 |
-10.16434 |
41.063779 |
|
8.5 |
0.3641116 |
-9.53326 |
46.198039 |
|
9 |
0.3182904 |
-9.18969 |
53.775743 |
|
9.5 |
0.2755685 |
-8.63369 |
57.426075 |
|
10 |
0.2399440 |
-8.13658 |
60.661692 |
|
10.5 |
0.2143400 |
-7.92362 |
66.762776 |
|
11 |
0.1898436 |
-7.53188 |
69.147928 |
|
11.5 |
0.1702469 |
-7.24105 |
72.098944 |
|
12 |
0.1547097 |
-7.04126 |
75.631936 |
|
12.5 |
0.1412861 |
-6.83930 |
78.336747 |
|
13 |
0.1217255 |
-5.97703 |
66.91764 |
|
13.5 |
0.1232893 |
-6.69998 |
86.25306 |
|
14 |
0.1175103 |
-6.72683 |
91.21569 |
|
14.5 |
0.1136359 |
-6.81993 |
96.934486 |
|
15 |
0.1113080 |
-6.96372 |
103.14859 |
|
15.5 |
0.1108260 |
-7.19011 |
110.49047 |
|
16 |
0.1125514 |
-7.53825 |
119.82293 |
|
16.5 |
0.1172714 |
-8.09136 |
133.20144 |
|
17 |
0.1239331 |
-8.76870 |
148.90028 |
|
17.5 |
0.1333155 |
-9.66441 |
169.41517 |
|
18 |
0.1427915 |
-10.54996 |
189.66513 |
51 to 95th%ile
|
Age in years |
wgt^2 |
wgt |
constant |
|---|---|---|---|
|
2 |
-5.561251 |
163.52409 |
-1105.282 |
|
2.5 |
-3.072597 |
105.11427 |
-798.0938 |
|
3 |
-2.200349 |
83.514386 |
-690.2418 |
|
3.5 |
-2.000489 |
80.265859 |
-705.4317 |
|
4 |
-1.897658 |
79.544148 |
-736.2567 |
|
4.5 |
-1.771493 |
77.586885 |
-753.6931 |
|
5 |
-1.611547 |
73.940203 |
-753.0868 |
|
5.5 |
-1.424622 |
68.79589 |
-735.8472 |
|
6 |
-1.195728 |
61.215904 |
-688.906 |
|
6.5 |
-0.986584 |
53.839292 |
-639.9887 |
|
7 |
-0.778141 |
45.673991 |
-575.7535 |
|
7.5 |
-0.604984 |
38.443126 |
-516.2876 |
|
8 |
-0.464381 |
32.094894 |
-460.1718 |
|
8.5 |
-0.357903 |
26.957371 |
-413.2148 |
|
9 |
-0.280858 |
23.021182 |
-377.2967 |
|
9.5 |
-0.223381 |
19.888397 |
-348.1342 |
|
10 |
-0.182870 |
17.599075 |
-328.7838 |
|
10.5 |
-0.153289 |
15.862789 |
-315.6743 |
|
11 |
-0.131765 |
14.579374 |
-308.5315 |
|
11.5 |
-0.117100 |
13.751174 |
-308.9642 |
|
12 |
-0.106906 |
13.237188 |
-315.0698 |
|
12.5 |
-0.100655 |
13.048477 |
-328.2787 |
|
13 |
-0.096778 |
13.058944 |
-345.9815 |
|
13.5 |
-0.094109 |
13.159671 |
-365.488 |
|
14 |
-0.092784 |
13.376893 |
-387.528 |
|
14.5 |
-0.091831 |
13.595483 |
-408.4668 |
|
15 |
-0.091381 |
13.830368 |
-428.4031 |
|
15.5 |
-0.091206 |
14.044876 |
-445.6037 |
|
16 |
-0.091022 |
14.19387 |
-458.0478 |
|
16.5 |
-0.090764 |
14.263599 |
-464.898 |
|
17 |
-0.090735 |
14.308162 |
-468.4299 |
|
17.5 |
-0.090694 |
14.308226 |
-468.6053 |
|
18 |
-0.091117 |
14.348678 |
-469.1726 |
