Child Growth Percentile worksheet

1. Height-for-age percentile: 36

1. Find the age in months, because the CDC tables go month by month

   $8\text{\hspace{0.17em}years}\times 12+9$$=105\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{130\text{\hspace{0.17em}cm}}{132.155}\right)}^{0.403268}-1}{0.403268\times 0.045856}$$=\mathrm{-0.357}$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-0.357}\right)\times 100$$=36$

4. Read the CDC weight-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{22\text{\hspace{0.17em}kg}}{27.7835}\right)}^{\mathrm{-1.357502}}-1}{\mathrm{-1.357502}\times 0.163309}$$=\mathrm{-1.682}$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-1.682}\right)\times 100$$=4.6$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{22\text{\hspace{0.17em}kg}}{{\left(1.3\text{\hspace{0.17em}m}\right)}^2}$$=13.02\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{13.02\text{\hspace{0.17em}kg/m²}}{16.0444}\right)}^{\mathrm{-3.034348}}-1}{\mathrm{-3.034348}\times 0.109006}$$=\mathrm{-2.678}$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-2.678}\right)\times 100$$=0.4$

2. Height-for-age percentile: 0.5

1. Find the age in months, because the CDC tables go month by month

   $4\text{\hspace{0.17em}years}\times 12+0$$=48\text{\hspace{0.17em}months}$

2. Change height to centimeters and weight to kilograms, the units in the CDC tables (1 in = 2.54 cm, 1 lb = 0.45359237 kg)

   $36\text{\hspace{0.17em}in}\times 2.54=91.44\text{\hspace{0.17em}cm}\text{;}28\text{\hspace{0.17em}lb}\times 0.45359237=12.701\text{\hspace{0.17em}kg}$

3. Read the CDC height-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{91.44\text{\hspace{0.17em}cm}}{102.2239}\right)}^{0.792898}-1}{0.792898\times 0.041298}$$=\mathrm{-2.584}$

4. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-2.584}\right)\times 100$$=0.5$

5. Read the CDC weight-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{12.7\text{\hspace{0.17em}kg}}{16.2311}\right)}^{\mathrm{-0.908375}}-1}{\mathrm{-0.908375}\times 0.119562}$$=\mathrm{-2.298}$

6. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-2.298}\right)\times 100$$=1.1$

7. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{12.701\text{\hspace{0.17em}kg}}{{\left(0.9144\text{\hspace{0.17em}m}\right)}^2}$$=15.19\text{\hspace{0.17em}kg/m²}$

8. Read the CDC BMI-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{15.19\text{\hspace{0.17em}kg/m²}}{15.6406}\right)}^{\mathrm{-1.684301}}-1}{\mathrm{-1.684301}\times 0.07181}$$=\mathrm{-0.418}$

9. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-0.418}\right)\times 100$$=33.8$

3. Height-for-age percentile: 100

1. Find the age in months, because the CDC tables go month by month

   $4\text{\hspace{0.17em}years}\times 12+0$$=48\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{130\text{\hspace{0.17em}cm}}{100.751}\right)}^{0.238432}-1}{0.238432\times 0.043209}$$=6.082$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(6.082\right)\times 100$$=100$

4. Read the CDC weight-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{22.5\text{\hspace{0.17em}kg}}{15.7932}\right)}^{\mathrm{-1.171494}}-1}{\mathrm{-1.171494}\times 0.131345}$$=2.206$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.206\right)\times 100$$=98.6$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{22.5\text{\hspace{0.17em}kg}}{{\left(1.3\text{\hspace{0.17em}m}\right)}^2}$$=13.31\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{13.31\text{\hspace{0.17em}kg/m²}}{15.3101}\right)}^{\mathrm{-2.990551}}-1}{\mathrm{-2.990551}\times 0.078596}$$=\mathrm{-2.207}$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-2.207}\right)\times 100$$=1.4$

4. Height-for-age percentile: 0.9

1. Find the age in months, because the CDC tables go month by month

   $3\text{\hspace{0.17em}years}\times 12+3$$=39\text{\hspace{0.17em}months}$

2. Change height to centimeters and weight to kilograms, the units in the CDC tables (1 in = 2.54 cm, 1 lb = 0.45359237 kg)

   $34\text{\hspace{0.17em}in}\times 2.54=86.36\text{\hspace{0.17em}cm}\text{;}34\text{\hspace{0.17em}lb}\times 0.45359237=15.422\text{\hspace{0.17em}kg}$

3. Read the CDC height-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{86.36\text{\hspace{0.17em}cm}}{95.6604}\right)}^{0.46916}-1}{0.46916\times 0.04225}$$=\mathrm{-2.364}$

4. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-2.364}\right)\times 100$$=0.9$

5. Read the CDC weight-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{15.42\text{\hspace{0.17em}kg}}{14.3264}\right)}^{\mathrm{-1.060993}}-1}{\mathrm{-1.060993}\times 0.12224}$$=0.58$

6. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(0.58\right)\times 100$$=71.9$

7. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{15.422\text{\hspace{0.17em}kg}}{{\left(0.8636\text{\hspace{0.17em}m}\right)}^2}$$=20.68\text{\hspace{0.17em}kg/m²}$

8. Read the CDC BMI-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{20.68\text{\hspace{0.17em}kg/m²}}{15.5932}\right)}^{\mathrm{-2.324362}}-1}{\mathrm{-2.324362}\times 0.078128}$$=2.649$

9. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.649\right)\times 100$$=99.6$

5. Height-for-age percentile: 80.5

1. Find the age in months, because the CDC tables go month by month

   $4\text{\hspace{0.17em}years}\times 12+9$$=57\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{110\text{\hspace{0.17em}cm}}{105.9121}\right)}^{0.017197}-1}{0.017197\times 0.044019}$$=0.861$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(0.861\right)\times 100$$=80.5$

4. Read the CDC weight-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{27.5\text{\hspace{0.17em}kg}}{17.3796}\right)}^{\mathrm{-1.260629}}-1}{\mathrm{-1.260629}\times 0.138691}$$=2.512$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.512\right)\times 100$$=99.4$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{27.5\text{\hspace{0.17em}kg}}{{\left(1.1\text{\hspace{0.17em}m}\right)}^2}$$=22.73\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{22.73\text{\hspace{0.17em}kg/m²}}{15.1711}\right)}^{\mathrm{-3.313206}}-1}{\mathrm{-3.313206}\times 0.082189}$$=2.71$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.71\right)\times 100$$=99.7$

6. Height-for-age percentile: 100

1. Find the age in months, because the CDC tables go month by month

   $3\text{\hspace{0.17em}years}\times 12+0$$=36\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{130\text{\hspace{0.17em}cm}}{93.9236}\right)}^{0.560769}-1}{0.560769\times 0.041995}$$=8.491$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(8.491\right)\times 100$$=100$

4. Read the CDC weight-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{20\text{\hspace{0.17em}kg}}{13.8652}\right)}^{\mathrm{-1.016556}}-1}{\mathrm{-1.016556}\times 0.118939}$$=2.572$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.572\right)\times 100$$=99.5$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{20\text{\hspace{0.17em}kg}}{{\left(1.3\text{\hspace{0.17em}m}\right)}^2}$$=11.83\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{11.83\text{\hspace{0.17em}kg/m²}}{15.7222}\right)}^{\mathrm{-2.050063}}-1}{\mathrm{-2.050063}\times 0.078741}$$=\mathrm{-4.896}$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-4.896}\right)\times 100$$=4.9e-5$

7. Height-for-age percentile: 1.25e-14

1. Find the age in months, because the CDC tables go month by month

   $16\text{\hspace{0.17em}years}\times 12+0$$=192\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{90\text{\hspace{0.17em}cm}}{173.5057}\right)}^{2.125774}-1}{2.125774\times 0.043182}$$=\mathrm{-8.195}$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-8.195}\right)\times 100$$=1.25e-14$

4. Read the CDC weight-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{20\text{\hspace{0.17em}kg}}{60.9212}\right)}^{\mathrm{-0.794905}}-1}{\mathrm{-0.794905}\times 0.17281}$$=\mathrm{-10.366}$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-10.366}\right)\times 100$$=1.77e-23$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{20\text{\hspace{0.17em}kg}}{{\left(0.9\text{\hspace{0.17em}m}\right)}^2}$$=24.69\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{24.69\text{\hspace{0.17em}kg/m²}}{20.5287}\right)}^{\mathrm{-2.042882}}-1}{\mathrm{-2.042882}\times 0.134245}$$=1.146$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(1.146\right)\times 100$$=87.4$

8. Height-for-age percentile: 98

1. Find the age in months, because the CDC tables go month by month

   $4\text{\hspace{0.17em}years}\times 12+0$$=48\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{110\text{\hspace{0.17em}cm}}{100.751}\right)}^{0.238432}-1}{0.238432\times 0.043209}$$=2.054$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.054\right)\times 100$$=98$

4. Read the CDC weight-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{19\text{\hspace{0.17em}kg}}{15.7932}\right)}^{\mathrm{-1.171494}}-1}{\mathrm{-1.171494}\times 0.131345}$$=1.265$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(1.265\right)\times 100$$=89.7$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{19\text{\hspace{0.17em}kg}}{{\left(1.1\text{\hspace{0.17em}m}\right)}^2}$$=15.7\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{15.7\text{\hspace{0.17em}kg/m²}}{15.3101}\right)}^{\mathrm{-2.990551}}-1}{\mathrm{-2.990551}\times 0.078596}$$=0.31$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(0.31\right)\times 100$$=62.2$

9. Height-for-age percentile: 1.6

1. Find the age in months, because the CDC tables go month by month

   $5\text{\hspace{0.17em}years}\times 12+6$$=66\text{\hspace{0.17em}months}$

2. Change height to centimeters and weight to kilograms, the units in the CDC tables (1 in = 2.54 cm, 1 lb = 0.45359237 kg)

   $40\text{\hspace{0.17em}in}\times 2.54=101.6\text{\hspace{0.17em}cm}\text{;}38\text{\hspace{0.17em}lb}\times 0.45359237=17.237\text{\hspace{0.17em}kg}$

3. Read the CDC height-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{101.6\text{\hspace{0.17em}cm}}{112.1593}\right)}^{1.260565}-1}{1.260565\times 0.043135}$$=\mathrm{-2.155}$

4. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-2.155}\right)\times 100$$=1.6$

5. Read the CDC weight-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{17.24\text{\hspace{0.17em}kg}}{19.526}\right)}^{\mathrm{-1.031643}}-1}{\mathrm{-1.031643}\times 0.134287}$$=\mathrm{-0.991}$

6. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-0.991}\right)\times 100$$=16.1$

7. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{17.237\text{\hspace{0.17em}kg}}{{\left(1.016\text{\hspace{0.17em}m}\right)}^2}$$=16.7\text{\hspace{0.17em}kg/m²}$

8. Read the CDC BMI-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{16.7\text{\hspace{0.17em}kg/m²}}{15.3813}\right)}^{\mathrm{-2.955819}}-1}{\mathrm{-2.955819}\times 0.07892}$$=0.924$

9. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(0.924\right)\times 100$$=82.2$

10. Height-for-age percentile: 100

1. Find the age in months, because the CDC tables go month by month

   $2\text{\hspace{0.17em}years}\times 12+0$$=24\text{\hspace{0.17em}months}$

2. Read the CDC height-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{100\text{\hspace{0.17em}cm}}{84.9756}\right)}^{1.072449}-1}{1.072449\times 0.040791}$$=4.361$

3. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(4.361\right)\times 100$$=100$

4. Read the CDC weight-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{16\text{\hspace{0.17em}kg}}{12.055}\right)}^{\mathrm{-0.73534}}-1}{\mathrm{-0.73534}\times 0.107399}$$=2.38$

5. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(2.38\right)\times 100$$=99.1$

6. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

   $\frac{16\text{\hspace{0.17em}kg}}{{\left(1\text{\hspace{0.17em}m}\right)}^2}$$=16\text{\hspace{0.17em}kg/m²}$

7. Read the CDC BMI-for-age values for a girl of this age. M is the middle (median) value, and L and S set the curve's shape and spread

   $z$$=\frac{{\left(\frac{16\text{\hspace{0.17em}kg/m²}}{16.4234}\right)}^{\mathrm{-0.986609}}-1}{\mathrm{-0.986609}\times 0.085452}$$=\mathrm{-0.31}$

8. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

   $\Phi \left(\mathrm{-0.31}\right)\times 100$$=37.8$