### Description

The distribution of body lengths for young boys age 0-3 years can be used to evaluate the physical development of a child.

Data: body length in centimeters

month

5th%

10th%

25th%

50th%

75th%

90th%

95th%

0

46.4

47.5

49

50.5

51.8

53.5

54.4

1

50.4

51.3

53

54.6

56.2

57.7

58.6

3

56.7

57.7

59.4

61.1

63

64.5

65.4

6

63.4

64.4

66.1

67.8

69.7

71.3

72.3

9

68

69.1

70.6

72.3

74

75.9

77.1

12

71.7

72.8

74.3

76.1

77.7

79.8

81.2

18

77.5

78.7

80.5

82.4

84.3

86.6

88.1

24

82.3

83.5

85.6

87.6

89.9

92.2

93.8

30

87

88.2

90.1

92.3

94.6

97

98.7

36

91.2

92.4

94.2

96.5

98.9

101.4

103.1

Polynomial equations approximating this data were calculated in JMP, as follows:

5th% for height in centimeters =

= ((0.0000024 * ((months)^5)) - (0.000276 * ((months)^4)) + (0.0125091 * ((months)^3)) - (0.0283668 * ((months)^2)) + (4.1308165 * (months)) + 46.475371)

10th% for height in centimeters =

((0.0000022 * ((months)^5)) - (0.000255 * ((months)^4)) + (0.0117252 * ((months)^3)) - (0.271785 * ((months)^2)) + (4.0761928 * (months)) + 47.516595)

25th% for height in centimeters =

= ((0.0000034 * ((months)^5)) - (0.000369 * ((months)^4)) + (0.0152959 * ((months)^3)) - (0.315487 * ((months)^2)) + (4.2560769 * (months)) + 49.03369)

50th% for height in centimeters =

= ((0.0000036 * ((months)^5)) - (0.000383 * ((months)^4)) + (0.015837 * ((months)^3)) - (0.324105 * ((months)^2)) + (4.3236754 * (months)) + 50.557971)

75th% for height in centimeters =

= ((0.0000052 * ((months)^5)) - (0.000537 * ((months)^4)) + (0.0210058 * ((months)^3)) - (0.395614 * ((months)^2)) + (4.6958102 * (months)) + 51.856726)

90th% for height in centimeters =

= ((0.0000044 * ((months)^5)) - (0.000462 * ((months)^4)) + (0.0183207 * ((months)^3)) - (0.356203 * ((months)^2)) + (4.5313743 * (months)) + 53.531472)

95th% for height  in centimeters=

= ((0.000004 * ((months)^5)) - (0.00042 * ((months)^4)) + (0.0169116 * ((months)^3)) - (0.336706 * ((months)^2)) + (4.4751708 * (months)) + 54.448242)

Distribution of Body Length 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.

0 to 3 years, 5 to 50%ile

Age in years

hgt^2

hgt in cm

coefficient

0

2.1719982

-199.5039

4585.7866

0.08

1.8048251

-178.8858

4436.5734

0.25

1.6248840

-181.2205

5056.4876

0.5

1.6248840

-202.9939

6343.6060

0.75

1.7022011

-228.2909

7657.6283

1

1.5040825

-211.9857

7471.7798

1.5

1.3344506

-204.1846

7814.2288

2

1.1693594

-190.2422

7741.7320

2.5

0.9598316

-163.5627

6969.8213

3

0.8580308

-152.4731

6773.5848

0 to 3 years, 51 to 95%ile

Age in years

hgt^2

hgt in cm

coefficient

0

-2.635121

287.691660

-7757.814

0.08

-1.826629

218.028120

-6408.868

0.25

-1.190374

161.135190

-5351.538

0.5

-1.267332

187.616000

-6844.720

0.75

-1.624136

251.928410

-9674.425

1

-1.712555

278.013820

-11188.640

1.5

-1.266565

223.721470

-9784.688

2

-0.916428

173.486250

-8114.923

2.5

-0.911607

181.118710

-8900.942

3

-0.833547

173.163950

-8898.052