The distribution of height for boys age 2-18 years can be used to evaluate the physical development of a child.
Data: height in centimeters.
|
year |
5th% |
10th% |
25th% |
50th% |
75th% |
90th% |
95th% |
|---|---|---|---|---|---|---|---|
|
2 |
82.5 |
83.5 |
85.3 |
86.8 |
89.2 |
92 |
94.4 |
|
2.5 |
85.4 |
86.5 |
88.5 |
90.4 |
92.9 |
95.6 |
97.8 |
|
3 |
89 |
90.3 |
92.6 |
94.9 |
97.5 |
100.1 |
102 |
|
3.5 |
92.5 |
93.9 |
96.4 |
99.1 |
101.7 |
104.3 |
106.1 |
|
4 |
95.8 |
97.3 |
100 |
102.9 |
105.7 |
108.2 |
109.9 |
|
4.5 |
98.9 |
100.6 |
103.4 |
106.6 |
109.4 |
111.9 |
113.5 |
|
5 |
102 |
103.7 |
106.5 |
109.9 |
112.8 |
115.4 |
117 |
|
5.5 |
104.9 |
106.7 |
109.6 |
113.1 |
116.1 |
118.7 |
120.3 |
|
6 |
107.7 |
109.6 |
112.5 |
116.1 |
119.2 |
121.9 |
123.5 |
|
6.5 |
110.4 |
112.3 |
115.3 |
119 |
122.2 |
124.9 |
126.6 |
|
7 |
113 |
115 |
118 |
121.7 |
125 |
127.9 |
129.7 |
|
7.5 |
115.6 |
117.6 |
120.6 |
124.4 |
127.8 |
130.8 |
132.7 |
|
8 |
118.1 |
120.2 |
123.2 |
127 |
130.5 |
133.6 |
135.7 |
|
8.5 |
120.5 |
122.7 |
125.7 |
129.6 |
133.2 |
136.5 |
138.8 |
|
9 |
122.9 |
125.2 |
128.2 |
132.2 |
136 |
139.4 |
141.8 |
|
9.5 |
125.3 |
127.6 |
130.8 |
134.8 |
138.8 |
142.4 |
144.9 |
|
10 |
127.7 |
130.1 |
133.4 |
137.5 |
141.6 |
145.5 |
148.1 |
|
10.5 |
130.1 |
132.6 |
136 |
140.3 |
144.6 |
148.7 |
151.5 |
|
11 |
132.6 |
135.1 |
138.7 |
143.33 |
147.8 |
152.1 |
154.9 |
|
11.5 |
135 |
137.7 |
141.5 |
146.4 |
151.1 |
155.6 |
158.5 |
|
12 |
137.6 |
140.3 |
144.4 |
149.7 |
154.6 |
159.4 |
162.3 |
|
12.5 |
140.2 |
143 |
147.4 |
153 |
158.2 |
163.2 |
166.1 |
|
13 |
142.9 |
145.8 |
150.5 |
156.5 |
161.8 |
167 |
169.8 |
|
13.5 |
145.7 |
148.7 |
153.6 |
159.9 |
165.3 |
170.5 |
173.4 |
|
14 |
148.8 |
151.8 |
156.9 |
163.1 |
168.5 |
173.8 |
176.7 |
|
14.5 |
152 |
155 |
160.1 |
166.2 |
171.5 |
176.6 |
179.5 |
|
15 |
155.2 |
158.2 |
163.3 |
169 |
174.1 |
178.9 |
181.9 |
|
15.5 |
158.3 |
161.2 |
166.2 |
171.5 |
176.3 |
180.8 |
183.9 |
|
16 |
161.1 |
163.9 |
168.7 |
173.5 |
178.1 |
182.4 |
185.4 |
|
16.5 |
163.4 |
166.1 |
170.6 |
175.2 |
179.5 |
183.6 |
186.6 |
|
17 |
164.9 |
167.7 |
171.9 |
176.2 |
180.5 |
184.4 |
187.3 |
|
17.5 |
165.6 |
168.5 |
172.4 |
176.7 |
181 |
185 |
187.6 |
|
18 |
165.7 |
168.7 |
172.3 |
176.8 |
181.2 |
185.3 |
187.6 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for height in centimeters =
= ((-0.000453 * ((years)^5)) + (0.0201607 * ((years)^4)) - (0.316331 * ((years)^3)) + (2.0319664 * ((years)^2)) + (0.9485411 * (years)) + 74.77485))
10th% for height in centimeters =
= ((-0.000413 * ((years)^5)) + (0.0180759 * ((years)^4)) - (0.27654 * ((years)^3)) + (1.6840491 * ((years)^2)) + (2.4810422 * (years)) + 73.725244))
25th% for height in centimeters =
= ((-0.00039 * ((years)^5)) + (0.0160131 * ((years)^4)) - (0.221666 * ((years)^3)) + (1.092761 * ((years)^2)) + (5.2799122 * (years)) + 71.720775))
50th% for height in centimeters =
= ((-0.000251 * ((years)^5)) + (0.0083147 * ((years)^4)) - (0.066047 * ((years)^3)) - (0.325854 * ((years)^2)) + (11.294887 * (years)) + 65.382471))
75th% for height in centimeters =
= ((-0.000155 * ((years)^5)) + (0.0034172 * ((years)^4)) + (0.0232615 * ((years)^3)) - (1.033526 * ((years)^2)) + (13.879486 * (years)) + 64.648641))
90th% for height in centimeters =
= ((-0.000045 * ((years)^5)) - (0.002031 * ((years)^4)) + (0.1177074 * ((years)^3)) - (1.712467 * ((years)^2)) + (15.911949 * (years)) + 65.259011))
95th% for height in centimeters =
= ((-0.000077 * ((years)^5)) - (0.000241 * ((years)^4)) + (0.0764447 * ((years)^3)) - (1.250146 * ((years)^2)) + (13.643516 * (years)) + 70.762727))
Distribution of Height 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.
2 to 18 years, 5 to 50%ile
|
2-18 years |
hgt^2 |
hgt in cm |
coefficient |
|---|---|---|---|
|
2 |
2.0347000 |
-334.1858 |
13726.9060 |
|
2.5 |
1.2875406 |
-217.4179 |
9182.4864 |
|
3 |
0.8799624 |
-154.2295 |
6761.3718 |
|
3.5 |
0.6255558 |
-113.039 |
5108.6976 |
|
4 |
0.5418730 |
-101.3354 |
4739.8329 |
|
4.5 |
0.4488957 |
-86.38041 |
4157.1500 |
|
5 |
0.3856063 |
-75.97498 |
3742.3758 |
|
5.5 |
0.3691776 |
-74.95506 |
3805.1260 |
|
6 |
0.3529142 |
-73.57702 |
3835.4004 |
|
6.5 |
0.3295741 |
-70.32898 |
3752.1509 |
|
7 |
0.3381396 |
-74.14276 |
4065.1405 |
|
7.5 |
0.3159975 |
-70.67419 |
3951.8214 |
|
8 |
0.3241707 |
-74.34371 |
4263.2432 |
|
8.5 |
0.3112781 |
-72.84415 |
4262.4928 |
|
9 |
0.2993295 |
-71.45267 |
4264.9009 |
|
9.5 |
0.2980996 |
-72.74913 |
4439.9476 |
|
10 |
0.2859228 |
-71.18731 |
4432.6720 |
|
10.5 |
0.2595245 |
-65.71392 |
4161.3154 |
|
11 |
0.2157174 |
-55.2817 |
3542.0829 |
|
11.5 |
0.1947127 |
-50.79862 |
3313.8007 |
|
12 |
0.1592378 |
-41.99004 |
2767.5059 |
|
12.5 |
0.1413415 |
-37.89204 |
2538.9327 |
|
13 |
0.1206326 |
-32.77816 |
2225.3245 |
|
13.5 |
0.1082713 |
-29.8891 |
2061.0900 |
|
14 |
0.1140136 |
-32.39413 |
2300.6091 |
|
14.5 |
0.1190367 |
-34.69071 |
2527.5774 |
|
15 |
0.1410119 |
-42.44726 |
3196.1772 |
|
15.5 |
0.1650560 |
-51.02812 |
3946.6474 |
|
16 |
0.2034486 |
-64.45822 |
5109.1878 |
|
16.5 |
0.2224873 |
-71.52833 |
5752.4787 |
|
17 |
0.2606202 |
-84.91775 |
6921.1694 |
|
17.5 |
0.2674331 |
-87.4694 |
7155.8841 |
|
18 |
0.2505486 |
-81.71061 |
6664.9156 |
2 to 18 years, 51 to 95%ile
|
2-18 years |
hgt^2 |
hgt in cm |
coefficient |
|---|---|---|---|
|
2 |
-0.801282 |
151.045970 |
-7023.482 |
|
2.5 |
-0.769695 |
150.902980 |
-7301.441 |
|
3 |
-0.722567 |
148.603870 |
-7545.041 |
|
3.5 |
-0.716582 |
153.460450 |
-8120.489 |
|
4 |
-0.613978 |
137.112490 |
-7557.889 |
|
4.5 |
-0.601813 |
139.005570 |
-7929.305 |
|
5 |
-0.554088 |
132.079770 |
-7773.327 |
|
5.5 |
-0.511507 |
125.665010 |
-7619.777 |
|
6 |
-0.472726 |
119.369690 |
-7436.895 |
|
6.5 |
-0.448668 |
116.151130 |
-7418.481 |
|
7 |
-0.426420 |
112.850410 |
-7368.284 |
|
7.5 |
-0.405276 |
109.641150 |
-7317.623 |
|
8 |
-0.391888 |
108.146780 |
-7363.959 |
|
8.5 |
-0.375272 |
105.631120 |
-7336.721 |
|
9 |
-0.337298 |
97.130098 |
-6895.764 |
|
9.5 |
-0.303142 |
89.263817 |
-6474.424 |
|
10 |
-0.286626 |
86.109401 |
-6371.040 |
|
10.5 |
-0.262059 |
80.490792 |
-6084.483 |
|
11 |
-0.239908 |
75.437204 |
-5833.859 |
|
11.5 |
-0.216415 |
69.704550 |
-5516.326 |
|
12 |
-0.196423 |
64.848245 |
-5255.897 |
|
12.5 |
-0.172183 |
58.373291 |
-4850.470 |
|
13 |
-0.163234 |
56.633908 |
-4815.180 |
|
13.5 |
-0.158018 |
55.993329 |
-4863.096 |
|
14 |
-0.157906 |
56.953338 |
-5038.496 |
|
14.5 |
-0.164886 |
60.378209 |
-5430.277 |
|
15 |
-0.182016 |
67.360041 |
-6135.311 |
|
15.5 |
-0.210686 |
78.514453 |
-7218.506 |
|
16 |
-0.230099 |
86.373145 |
-8009.271 |
|
16.5 |
-0.265932 |
100.168080 |
-9336.698 |
|
17 |
-0.267433 |
101.284880 |
-9493.626 |
|
17.5 |
-0.258421 |
98.278899 |
-9247.249 |
|
18 |
-0.236197 |
90.235157 |
-8520.472 |
