The distribution of height for girls 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 |
81.6 |
82.1 |
84 |
86.8 |
89.3 |
92 |
93.6 |
|
2.5 |
84.6 |
85.3 |
87.3 |
90 |
92.5 |
95 |
96.6 |
|
3 |
88.3 |
89.3 |
91.4 |
94.1 |
96.6 |
99 |
100.6 |
|
3.5 |
91.7 |
93 |
95.2 |
97.9 |
100.5 |
102.8 |
104.5 |
|
4 |
95 |
96.4 |
98.8 |
101.6 |
104.3 |
106.6 |
108.3 |
|
4.5 |
98.1 |
99.7 |
102.2 |
105 |
107.9 |
110.2 |
112 |
|
5 |
101.1 |
102.7 |
105.4 |
108.4 |
111.4 |
113.8 |
115.6 |
|
5.5 |
103.9 |
105.6 |
108.4 |
111.6 |
114.8 |
117.4 |
119.2 |
|
6 |
106.6 |
108.4 |
111.3 |
114.6 |
118.1 |
120.8 |
122.7 |
|
6.5 |
109.2 |
111 |
114.1 |
117.6 |
121.3 |
124.2 |
126.1 |
|
7 |
111.8 |
113.6 |
116.8 |
120.6 |
124.4 |
127.6 |
129.5 |
|
7.5 |
114.4 |
116.2 |
119.5 |
123.5 |
127.5 |
130.9 |
132.9 |
|
8 |
116.9 |
118.7 |
122.2 |
126.4 |
130.6 |
134.2 |
136.2 |
|
8.5 |
119.5 |
121.3 |
124.9 |
129.3 |
133.6 |
137.4 |
139.6 |
|
9 |
122.1 |
123.9 |
127.7 |
132.2 |
136.7 |
140.7 |
142.9 |
|
9.5 |
124.8 |
126.6 |
130.6 |
135.2 |
139.8 |
143.9 |
146.2 |
|
10 |
127.5 |
129.5 |
133.6 |
138.3 |
142.9 |
147.2 |
149.5 |
|
10.5 |
130.4 |
132.5 |
136.7 |
141.5 |
146.1 |
150.4 |
152.8 |
|
11 |
133.5 |
135.6 |
140 |
144.8 |
149.3 |
153.7 |
156.2 |
|
11.5 |
136.6 |
139 |
143.5 |
148.2 |
152.6 |
156.9 |
159.5 |
|
12 |
139.8 |
142.3 |
147 |
151.5 |
155.8 |
160 |
162.7 |
|
12.5 |
142.7 |
145.4 |
150.1 |
154.6 |
158.8 |
162.9 |
165.6 |
|
13 |
145.2 |
148 |
152.8 |
157.1 |
161.3 |
165.3 |
168.1 |
|
13.5 |
147.2 |
150 |
154.7 |
159 |
163.2 |
167.3 |
170 |
|
14 |
148.7 |
151.5 |
155.9 |
160.4 |
164.6 |
168.7 |
171.3 |
|
14.5 |
149.7 |
152.5 |
156.8 |
161.2 |
165.6 |
169.8 |
172.2 |
|
15 |
150.5 |
153.2 |
157.2 |
161.8 |
166.3 |
170.5 |
172.8 |
|
15.5 |
151.1 |
153.6 |
157.5 |
162.1 |
166.7 |
170.9 |
173.1 |
|
16 |
151.6 |
154.1 |
157.8 |
162.4 |
166.9 |
171.1 |
173.3 |
|
16.5 |
152.2 |
154.6 |
158.2 |
162.7 |
167.1 |
171.2 |
173.4 |
|
17 |
152.7 |
155.1 |
158.7 |
163.1 |
167.3 |
171.2 |
173.5 |
|
17.5 |
153.2 |
155.6 |
159.1 |
163.4 |
167.5 |
171.1 |
173.5 |
|
18 |
153.6 |
156 |
159.6 |
163.7 |
167.6 |
171 |
173.6 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for height in centimeters =
= ((0.000379 * ((years)^5)) - (0.020908 * ((years)^4)) + (0.4121121 * ((years)^3)) - (3.664095 * ((years)^2)) + (20.207401 * (years)) + 51.80403))
10th% for height in centimeters =
= ((0.0004462 * ((years)^5)) - (0.024655 * ((years)^4)) + (0.4892741 * ((years)^3)) - (4.390184 * ((years)^2)) + (23.408942 * (years)) + 48.065278))
25th% for height in centimeters =
= ((0.0005347 * ((years)^5)) - (0.028842 * ((years)^4)) + (0.5594689 * ((years)^3)) - (4.906937 * ((years)^2)) + (25.328077 * (years)) + 47.578288))
50th% for height in centimeters =
= ((0.000463 * ((years)^5)) - (0.024821 * ((years)^4)) + (0.4748697 * ((years)^3)) - (4.108554 * ((years)^2)) + (22.3181 * (years)) + 53.971045))
75th% for height in centimeters =
= ((0.0003655 * ((years)^5)) - (0.019686 * ((years)^4)) + (0.374291 * ((years)^3)) - (3.231897 * ((years)^2)) + (19.304954 * (years)) + 59.857018))
90th% for height in centimeters =
= ((0.000294 * ((years)^5)) - (0.015675 * ((years)^4)) + (0.2881833 * ((years)^3)) - (2.383931 * ((years)^2)) + (15.84886 * (years)) + 66.867705))
95th% for height in centimeters =
= ((0.0003681 * ((years)^5)) - (0.01917 * ((years)^4)) + (0.3474993 * ((years)^3)) - (2.826709 * ((years)^2)) + (17.35826 * (years)) + 66.696338))
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
|
Age in years |
hgt^2 |
hgt in cm |
coefficient |
|---|---|---|---|
|
2.0 |
0.1149375 |
-10.78795 |
120.39022 |
|
2.5 |
0.3385397 |
-50.80054 |
1879.85950 |
|
3.0 |
0.4960976 |
-82.69822 |
3439.08720 |
|
3.5 |
0.5986562 |
-106.19780 |
4709.07480 |
|
4.0 |
0.5709657 |
-105.40410 |
4865.28150 |
|
4.5 |
0.6018133 |
-115.68180 |
5561.65060 |
|
5.0 |
0.5115263 |
-100.98650 |
4986.24110 |
|
5.5 |
0.4488957 |
-90.86937 |
4600.27440 |
|
6.0 |
0.4264204 |
-88.67586 |
4612.06080 |
|
6.5 |
0.3706127 |
-78.68329 |
4177.70340 |
|
7.0 |
0.3014982 |
-64.93161 |
3495.70500 |
|
7.5 |
0.2637066 |
-57.76712 |
3162.17240 |
|
8.0 |
0.2337036 |
-52.10832 |
2902.65100 |
|
8.5 |
0.2058285 |
-46.60322 |
2634.68640 |
|
9.0 |
0.1973033 |
-45.71525 |
2645.32540 |
|
9.5 |
0.1894671 |
-44.94145 |
2662.79250 |
|
10.0 |
0.1890093 |
-46.07170 |
2806.55620 |
|
10.5 |
0.1836944 |
-45.89056 |
2865.54460 |
|
11.0 |
0.1860822 |
-47.81484 |
3071.96840 |
|
11.5 |
0.2056233 |
-54.69255 |
3639.24950 |
|
12.0 |
0.2280889 |
-62.62543 |
4302.49440 |
|
12.5 |
0.2311958 |
-64.97758 |
4569.59140 |
|
13.0 |
0.2522492 |
-72.51362 |
5216.10810 |
|
13.5 |
0.2536163 |
-73.87794 |
5384.77780 |
|
14.0 |
0.2356256 |
-68.99043 |
5053.83410 |
|
14.5 |
0.2476847 |
-73.09574 |
5396.82390 |
|
15.0 |
0.2256597 |
-66.46806 |
4897.01500 |
|
15.5 |
0.2192825 |
-64.56243 |
4753.69630 |
|
16.0 |
0.2193436 |
-64.66778 |
4767.25410 |
|
16.5 |
0.2270218 |
-67.16268 |
4967.92740 |
|
17.0 |
0.2401421 |
-71.47306 |
5319.20050 |
|
17.5 |
0.2541801 |
-76.02132 |
5685.51000 |
|
18.0 |
0.2834858 |
-85.47155 |
6445.00100 |
ß2 o 18 Years, 51 to 95%ile
|
Age in years |
hgt^2 |
hgt in cm |
coefficient |
|---|---|---|---|
|
2.0 |
-0.7509920 |
142.042030 |
-6620.969 |
|
2.5 |
-0.7643160 |
149.422610 |
-7207.035 |
|
3.0 |
-0.7710900 |
157.056960 |
-7901.208 |
|
3.5 |
-0.7295610 |
154.521810 |
-8085.367 |
|
4.0 |
-0.6734340 |
148.123060 |
-8047.856 |
|
4.5 |
-0.5873820 |
133.966150 |
-7540.735 |
|
5.0 |
-0.5402620 |
127.337260 |
-7405.135 |
|
5.5 |
-0.4606500 |
112.294430 |
-6744.990 |
|
6.0 |
-0.3785610 |
95.453682 |
-5917.438 |
|
6.5 |
-0.3286520 |
85.440146 |
-5452.712 |
|
7.0 |
-0.3094450 |
82.475847 |
-5395.976 |
|
7.5 |
-0.2795410 |
76.484850 |
-5132.307 |
|
8.0 |
-0.2482090 |
69.787374 |
-4805.542 |
|
8.5 |
-0.2450110 |
70.264602 |
-4939.027 |
|
9.0 |
-0.2198140 |
64.683210 |
-4659.482 |
|
9.5 |
-0.2122950 |
63.838245 |
-4700.399 |
|
10.0 |
-0.2130340 |
65.323422 |
-4909.541 |
|
10.5 |
-0.2159800 |
67.542728 |
-5182.877 |
|
11.0 |
-0.2293950 |
72.984295 |
-5708.354 |
|
11.5 |
-0.2435930 |
78.928472 |
-6297.082 |
|
12.0 |
-0.2586210 |
85.272450 |
-6932.821 |
|
12.5 |
-0.2724850 |
91.337610 |
-7558.076 |
|
13.0 |
-0.2762030 |
93.917734 |
-7887.688 |
|
13.5 |
-0.2724850 |
93.735478 |
-7965.236 |
|
14.0 |
-0.2702650 |
93.770382 |
-8037.339 |
|
14.5 |
-0.2391300 |
83.811244 |
-7246.456 |
|
15.0 |
-0.2241910 |
79.101536 |
-6879.472 |
|
15.5 |
-0.2092880 |
74.241778 |
-6485.253 |
|
16.0 |
-0.2209320 |
78.288544 |
-6837.221 |
|
16.5 |
-0.2327930 |
82.442588 |
-7201.054 |
|
17.0 |
-0.2630980 |
92.888193 |
-8101.245 |
|
17.5 |
-0.2834860 |
99.984879 |
-8718.655 |
|
18.0 |
-0.3271650 |
114.930170 |
-9996.906 |
