### Description

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