Tanner and Davies reported data for height velocity shown by children in North America.
Age range for girls: 2.5 to 14.5 years
height velocity in cm per year =
= (change in height in cm over time interval) / ((time interval in months) / 12)
where:
• The average month length is 30.4 days.
• For accurate results there needs to be some constraints on the time interval between measurements. My guess is that it probably should be 6-12 months.
|
Age in |
Height Velocity in cm/year |
||||||
|---|---|---|---|---|---|---|---|
|
Years |
3%ile |
10%ile |
25%ile |
50%ile |
75%ile |
90%ile |
97%ile |
|
2.5 |
5.89 |
6.83 |
7.7 |
8.61 |
9.5 |
10.42 |
11.32 |
|
3 |
5.52 |
6.49 |
7.22 |
8.08 |
8.91 |
9.78 |
10.62 |
|
3.5 |
5.22 |
6 |
6.8 |
7.61 |
8.4 |
9.18 |
9.95 |
|
4 |
4.94 |
5.7 |
6.43 |
7.18 |
7.94 |
8.65 |
9.38 |
|
4.5 |
4.73 |
5.47 |
6.16 |
6.83 |
7.58 |
8.25 |
8.95 |
|
5 |
4.6 |
5.29 |
5.92 |
6.6 |
7.28 |
7.92 |
8.62 |
|
5.5 |
4.5 |
5.14 |
5.78 |
6.38 |
7.04 |
7.65 |
8.32 |
|
6 |
4.41 |
5.01 |
5.63 |
6.2 |
6.82 |
7.42 |
8.02 |
|
6.5 |
4.32 |
4.91 |
5.51 |
6.06 |
6.68 |
7.23 |
7.79 |
|
7 |
4.3 |
4.88 |
5.42 |
5.95 |
6.52 |
7.1 |
7.6 |
|
7.5 |
4.29 |
4.83 |
5.38 |
5.91 |
6.44 |
6.95 |
7.49 |
|
8 |
4.2 |
4.77 |
5.28 |
5.8 |
6.32 |
6.86 |
7.4 |
|
8.5 |
4.15 |
4.69 |
5.2 |
5.7 |
6.26 |
6.8 |
7.32 |
|
9 |
4.18 |
4.7 |
5.2 |
5.75 |
6.28 |
6.79 |
7.3 |
|
9.5 |
4.27 |
4.78 |
5.3 |
5.8 |
6.35 |
6.9 |
7.4 |
|
10 |
4.38 |
4.96 |
5.58 |
6.18 |
6.78 |
7.35 |
7.95 |
|
10.5 |
4.71 |
5.39 |
6.05 |
6.75 |
7.4 |
8.1 |
8.71 |
|
11 |
5.69 |
6.28 |
7 |
7.7 |
8.28 |
8.92 |
9.6 |
|
11.5 |
6.12 |
6.83 |
7.57 |
8.3 |
9 |
9.71 |
10.43 |
|
12 |
5.2 |
5.94 |
6.72 |
7.34 |
8.15 |
8.9 |
9.6 |
|
12.5 |
3.63 |
4.39 |
5.21 |
5.85 |
6.68 |
7.3 |
8.1 |
|
13 |
2.35 |
3 |
3.69 |
4.3 |
5 |
5.7 |
6.28 |
|
13.5 |
1.25 |
1.82 |
2.49 |
2.9 |
3.5 |
4.17 |
4.8 |
|
14 |
0.42 |
0.84 |
1.32 |
1.81 |
2.27 |
2.8 |
3.2 |
|
14.5 |
< 0.40 |
0.3 |
0.62 |
0.95 |
1.26 |
1.54 |
1.85 |
If this data in analyzed in JMP, the following polynomial equations are derived.
|
Age Range |
Percentile |
Equation with age in years |
|---|---|---|
|
2.5 to 9 |
3rd |
(-0.009161 * ((age)^3)) + (0.213272 * ((age)^2)) - (1.7153 * (age)) + 8.9895105 |
|
|
10th |
(-0.010053 * ((age)^3)) + (0.2401258 * ((age)^2)) - (1.993979* (age)) + 10.502928 |
|
|
25th |
(-0.010302 * ((age)^3)) + (0.2491047 * ((age)^2)) - (2.123389 * (age)) + 11.61541 |
|
|
50th |
(-0.009206 * ((age)^3)) + (0.2429259 * ((age)^2)) - (2.230099 * (age)) + 12.818328 |
|
|
75th |
(-0.00811 * ((age)^3)) + (0.2303185 * ((age)^2)) - (2.258046 * (age)) + 13.827014 |
|
|
90th |
(-0.009756 * ((age)^3)) + (0.2707898 * ((age)^2)) - (2.606553 * (age)) + 15.401551 |
|
|
97th |
(-0.009129 * ((age)^3)) + (0.2680849 * ((age)^2)) - (2.701403 * (age)) + 16.532892 |
|
9 to 11 |
3rd |
(0.42 * ((age)^3)) - (12.02857 * ((age)^2)) + (114.90643 * (age)) - 361.8469 |
|
|
10th |
(0.24 * ((age)^3)) - (6.665714 * ((age)^2)) + (61.864286 * (age)) - 187.1166 |
|
|
25th |
(0.2 * ((age)^3)) - 5.46 * ((age)^2)) + (49.9 * (age)) - 147.444 |
|
|
50th |
(0.033333 * ((age)^3)) - (0.431429 * ((age)^2)) - (0.429762 * (age)) + 20.258857 |
|
|
75th |
(-0.06667 * ((age)^3)) + (2.5171429 * ((age)^2)) - (29.27619 * (age)) + 114.47371 |
|
|
90th |
(-0.18 * ((age)^3)) + (5.8914286 * ((age)^2)) - (62.58357 * (age)) + 224.05914 |
|
|
97th |
(-0.21333 * ((age)^3)) + (6.9114286 * ((age)^2)) - (72.86524 * (age)) + 258.77914 |
|
11 to 12 |
3rd |
(-2.7 * ((age)^2)) + (61.61 * (age)) - 345.32 |
|
|
10th |
(-2.88 * ((age)^2)) + (65.9 * (age)) - 370.14 |
|
|
25th |
(-2.84 * ((age)^2)) + (65.04 * (age)) - 364.8 |
|
|
50th |
(-3.12 * ((age)^2)) + (71.4 * (age)) - 400.18 |
|
|
75th |
(-3.14 * ((age)^2)) + 72.09 * (age)) - 404.77 |
|
|
90th |
(-3.2 * ((age)^2)) + (73.58 * (age)) - 413.26 |
|
|
97th |
(-3.32 * ((age)^2)) + (76.36 * (age)) - 428.64 |
|
12 to 14.5 |
3rd |
(0.4742857 * ((age)^2)) - (14.71943 * (age)) +113.53114 |
|
|
10th |
(0.4778571 * ((age)^2)) - (14.95064 * (age)) + 116.56879 |
|
|
25th |
(0.3821429 * ((age)^2)) - (12.61079 * (age)) + 103.06264 |
|
|
50th |
(0.3564286 * ((age)^2)) - (12.04364 * (age)) + 100.60121 |
|
|
75th |
(0.2928571 * ((age)^2)) - (10.571 * (age)) + 92.914143 |
|
|
90th |
(0.1871429 * ((age)^2)) - (7.921 * (age)) + 77.029857 |
|
|
97th |
(0.1057143 * ((age)^2)) - (5.948857 * (age)) + 65.819143 |
