Tanner and Davies reported data for height velocity shown by children in North America.
Age range for boys: 2.5 to 17.5 years (limited to 17 years in the implementation)
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 |
Height Velocity in cm/year |
||||||
|---|---|---|---|---|---|---|---|
|
Years |
3%ile |
10%ile |
25%ile |
50%ile |
75%ile |
90%ile |
97%ile |
|
2.5 |
5.72 |
6.55 |
7.42 |
8.3 |
9.2 |
10.1 |
10.94 |
|
3 |
5.39 |
6.18 |
7 |
7.82 |
8.6 |
9.38 |
10.15 |
|
3.5 |
5.12 |
5.86 |
6.64 |
7.41 |
8.16 |
8.9 |
9.62 |
|
4 |
4.88 |
5.6 |
6.33 |
7.08 |
7.8 |
8.51 |
9.21 |
|
4.5 |
4.71 |
5.4 |
6.12 |
6.81 |
7.51 |
8.2 |
8.87 |
|
5 |
4.57 |
5.22 |
5.9 |
6.59 |
7.25 |
7.92 |
8.57 |
|
5.5 |
4.45 |
5.1 |
5.74 |
6.39 |
7.02 |
7.69 |
8.3 |
|
6 |
4.33 |
4.94 |
5.57 |
6.2 |
6.82 |
7.45 |
8.07 |
|
6.5 |
4.23 |
4.81 |
5.42 |
6.02 |
6.62 |
7.25 |
7.84 |
|
7 |
4.17 |
4.75 |
5.3 |
5.9 |
6.48 |
7.1 |
7.64 |
|
7.5 |
4.07 |
4.63 |
5.2 |
5.78 |
6.33 |
6.89 |
7.45 |
|
8 |
3.93 |
4.5 |
5.07 |
5.6 |
6.16 |
6.7 |
7.23 |
|
8.5 |
3.81 |
4.35 |
4.88 |
5.42 |
5.94 |
6.48 |
7 |
|
9 |
3.78 |
4.28 |
4.78 |
5.29 |
5.8 |
6.3 |
6.82 |
|
9.5 |
3.74 |
4.23 |
4.7 |
5.2 |
5.7 |
6.16 |
6.68 |
|
10 |
3.7 |
4.2 |
4.68 |
5.12 |
5.6 |
6.03 |
6.53 |
|
10.5 |
3.69 |
4.17 |
4.62 |
5.1 |
5.58 |
6 |
6.5 |
|
11 |
3.69 |
4.18 |
4.66 |
5.16 |
5.62 |
6.08 |
6.58 |
|
11.5 |
3.78 |
4.4 |
4.79 |
5.3 |
5.78 |
6.27 |
6.78 |
|
12 |
4.02 |
4.58 |
5.12 |
5.73 |
6.29 |
6.81 |
7.33 |
|
12.5 |
4.8 |
5.55 |
6.08 |
6.72 |
7.5 |
8.21 |
8.88 |
|
13 |
6.15 |
7 |
7.8 |
8.6 |
9.55 |
10.4 |
11.25 |
|
13.5 |
7.1 |
7.89 |
8.7 |
9.49 |
10.27 |
11.1 |
11.9 |
|
14 |
6.05 |
6.78 |
7.57 |
8.4 |
9.15 |
9.97 |
10.7 |
|
14.5 |
4.1 |
4.9 |
5.62 |
6.5 |
7.1 |
8 |
8.7 |
|
15 |
2.35 |
3.2 |
3.95 |
4.74 |
5.4 |
6.3 |
7 |
|
15.5 |
1.2 |
1.9 |
2.69 |
3.26 |
4.08 |
4.72 |
5.4 |
|
16 |
0.4 |
1 |
1.59 |
2.22 |
2.92 |
3.54 |
4.1 |
|
16.5 |
< 0.1 |
0.4 |
0.95 |
1.46 |
2.03 |
2.52 |
3 |
|
17 |
< 0.1 |
0.1 |
0.62 |
0.9 |
1.37 |
1.75 |
2.15 |
|
17.5 |
< 0.1 |
< 0.1 |
0.20 |
0.5 |
0.9 |
1.25 |
1.6 |
If this data in analyzed in JMP, the following polynomial equations are derived.
|
Age Range |
Percentile |
Equation with age in years |
|---|---|---|
|
2.5 to 10 |
3rd |
(-0.004452 * ((age)^3)) + (0.11284 * ((age)^2)) - (1.0965 * (age)) + 7.7888 |
|
|
10th |
(-0.004999 * ((age)^3)) + (0.1269399 * ((age)^2)) - (1.246484* (age)) + 8.9134975 |
|
|
25th |
(-0.005639 * ((age)^3)) + (0.142856 * ((age)^2)) - (1.414839 * (age)) + 10.113833 |
|
|
50th |
(-0.006907 * ((age)^3)) + (0.169811 * ((age)^2)) - (1.642173 * (age)) + 11.410698 |
|
|
75th |
(-0.00816 * ((age)^3)) + (0.1983368 * ((age)^2)) - (1.887257 * (age)) + 12.736175 |
|
|
90th |
(-0.010278 * ((age)^3)) + (0.23944 * ((age)^2)) - (2.1832 * (age)) + 14.11896 |
|
|
97th |
(-0.010817 * ((age)^3)) + (0.254959 * ((age)^2)) - (2.34955 * (age)) + 15.271678 |
|
10 to 13 |
3rd |
(0.22444 * ((age)^3)) - (7.2195 * ((age)^2)) + (77.31508 * (age)) - 271.9557 |
|
|
10th |
(0.226667 * ((age)^3)) - (7.24286 * ((age)^2)) + (77.08476 * (age)) - 269.0471 |
|
|
25th |
(0.266667 * ((age)^3)) - 8.538095 * ((age)^2)) + (91.019524 * (age)) - 318.3971 |
|
|
50th |
(0.286667 * ((age)^3)) - (9.18857 * ((age)^2)) + (98.118333 * (age)) - 343.8964 |
|
|
75th |
(0.302222 * ((age)^3)) - (9.6219 * ((age)^2)) + (102.03683 * (age)) - 354.8136 |
|
|
90th |
(0.317778* ((age)^3)) - (10.08714 * ((age)^2)) + (106.67413 * (age)) - 369.79 |
|
|
97th |
(0.353333 * ((age)^3)) - (11.23524* ((age)^2)) + (119.01214* (age)) - 413.4171 |
|
13 to 14 |
3rd |
(-4 * ((age)^2)) + (107.9 * (age)) - 720.55 |
|
|
10th |
(-4 * ((age)^2)) + (107.78 * (age)) - 718.14 |
|
|
25th |
(-4.06 * ((age)^2)) + (109.39 * (age)) - 728.13 |
|
|
50th |
(-3.96 * ((age)^2)) + (106.72 * (age)) - 709.52 |
|
|
75th |
(-3.38 * ((age)^2)) + (91.01 * (age)) - 602.36 |
|
|
90th |
(-3.66 * ((age)^2)) + (98.39 * (age)) - 650.13 |
|
|
97th |
(-3.7 * ((age)^2)) + (99.35 * (age)) - 655 |
|
14 to 17 |
3rd |
(0.8 * ((age)^2)) - (26.86 * (age)) + 225.31 |
|
|
10th |
(0.6857 * ((age)^2)) - (23.48 * (age)) + 201.1286 |
|
|
25th |
(0.64619 * ((age)^2)) - (22.3569 * (age)) + 193.92286 |
|
|
50th |
(0.564286 * ((age)^2)) - (20.01738 * (age)) + 178.0525 |
|
|
75th |
(0.512619 * ((age)^2)) - (18.47298 * (age)) + 167.23375 |
|
|
90th |
(0.4888 * ((age)^2)) - (17.89298 * (age)) + 164.67375 |
|
|
97th |
(0.463095 * ((age)^2)) - (17.2006 * (age)) + 160.75625 |
