### Description

The distribution of weight for a given height in girls from age 4 years to prepuberty can be used to evaluate the physical development of a child.

Data: height in centimeters and weight in kilograms.

length

5th%

10th%

25th%

50th%

75th%

90th%

95th%

90

11.45

11.67

12.28

13.14

14.11

14.98

15.74

92

11.86

12.1

12.74

13.63

14.63

15.57

16.42

94

12.26

12.53

13.21

14.12

15.14

16.13

17.05

96

12.66

12.97

13.7

14.62

15.66

16.69

17.65

98

13.06

13.42

14.19

15.13

16.19

17.24

18.23

100

13.48

13.88

14.69

15.65

16.73

17.8

18.8

102

13.91

14.36

15.21

16.2

17.28

18.38

19.38

104

14.36

14.85

15.75

16.75

17.86

18.98

19.98

106

14.84

15.37

16.3

17.33

18.46

19.62

20.61

108

15.35

15.91

16.87

17.94

19.09

20.3

21.29

110

15.9

16.48

17.47

18.56

19.76

21.03

22.03

112

16.48

17.09

18.08

19.22

20.47

21.81

22.84

114

17.11

17.72

18.72

19.91

21.23

22.67

23.73

116

17.77

18.4

19.4

20.64

22.04

23.6

24.71

118

18.48

19.11

20.11

21.42

22.92

24.62

25.81

120

19.22

19.85

20.87

22.25

23.88

25.73

27.03

122

19.99

20.64

21.68

23.13

24.91

26.95

28.37

124

20.8

21.47

22.54

24.09

26.05

28.27

29.87

126

21.65

22.34

23.47

25.11

27.28

29.71

31.51

128

22.53

23.25

24.46

26.22

28.63

31.28

33.33

130

23.44

24.22

25.52

27.4

30.09

32.99

35.33

132

24.38

25.22

26.66

28.68

31.68

34.84

37.53

134

25.35

26.28

27.88

30.06

33.41

36.84

39.93

136

26.34

27.39

29.19

31.54

35.29

39.01

42.54

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

5th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.0000247 * ((height in cm)^3)) - (0.004347 * ((height in cm)^2)) + (0.3462385 * (height in cm)) - 2.430703)

10th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.000045 * ((height in cm)^3)) - (0.011234 * ((height in cm)^2)) + (1.1314881 * (height in cm)) - 31.97981)

25th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.0000848 * ((height in cm)^3)) - (0.02435 * ((height in cm)^2)) + (2.5783033 * (height in cm)) - 84.39121)

50th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.0001012 * ((height in cm)^3)) - (0.029076 * ((height in cm)^2)) + (3.04138 * (height in cm)) - 98.88346)

75th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.0001522 * ((height in cm)^3)) - (0.044326 * ((height in cm)^2)) + (4.5682013 * (height in cm)) - 148.9818)

90th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.0001785 * ((height in cm)^3)) - (0.051505 * ((height in cm)^2)) + (5.2305385 * (height in cm)) - 168.692)

95th% of weight in kilograms for height in centimeters from 90 - 136 cm =

= ((0.0002599 * ((height in cm)^3)) - (0.077011 * ((height in cm)^2)) + (7.8924149 * (height in cm)) - 260.2659)

Distribution of Weight for Height

If the same data is analyzed for each month, then the percentile represented by a weight for 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.

>= 4 years, 5 to 50%ile

wgt^2

wgt

coefficient

90

2.9288203

-45.41748

141.09140

92

3.0280147

-51.76310

192.99520

94

3.4605960

-67.08499

307.28922

96

4.0617337

-87.83507

465.97933

98

4.3386455

-100.53060

577.85349

100

4.4279428

-108.21210

659.03482

102

4.3727600

-111.96470

716.26756

104

4.4613147

-119.94760

807.45428

106

4.2838279

-119.71210

838.07092

108

3.9935310

-115.53260

837.38985

110

3.8715719

-116.46970

878.04442

112

3.5470193

-110.12950

856.44950

114

3.1917465

-101.99080

815.47671

116

2.9167451

-96.22230

793.56786

118

2.5100425

-84.68278

712.37704

120

2.1630207

-74.67894

640.89894

122

1.9113350

-67.90295

598.17072

124

1.5929739

-57.63830

514.20033

126

1.3845571

-51.55847

471.78630

128

1.1669840

-44.53416

415.52251

130

1.0412208

-41.42204

403.38378

132

0.9200178

-38.22933

389.77609

134

0.8198029

-35.77032

384.58445

136

0.7431815

-34.28314

392.09002

138

140

142

144

>= 4 years, 51 to 95%ile

wgt^2

wgt

coefficient

90

-5.450236

174.820510

-1306.2230

92

-5.097557

169.371430

-1311.5990

94

-4.858160

166.815870

-1336.8860

96

-4.636192

164.469950

-1363.6030

98

-4.464659

163.465610

-1401.2110

100

-4.298985

162.393700

-1438.5550

102

-4.243756

165.125060

-1511.2660

104

-4.030757

161.971290

-1532.1250

106

-3.854043

159.914120

-1563.7900

108

-3.677700

157.657080

-1594.6470

110

-3.363668

149.441970

-1564.8610

112

-3.081426

141.967830

-1540.2120

114

-2.739822

131.264180

-1477.2500

116

-2.413451

120.410570

-1406.9580

118

-2.088068

108.767310

-1321.5680

120

-1.767510

96.422041

-1220.1720

122

-1.476261

84.521731

-1114.9870

124

-1.224165

73.765217

-1016.3990

126

-1.003930

63.811970

-919.1577

128

-0.820935

55.170029

-832.0313

130

-0.665159

47.368166

-748.3993

132

-0.540940

40.881099

-677.4451

134

-0.439934

35.342519

-614.8342

136

-0.356586

30.508832

-557.5376

138

140

142

144