The distribution of head circumference for young girls age 0-3 years can be used to evaluate the physical development of a child.
Data: head circumference in centimeters.
|
month |
5th% |
10th% |
25th% |
50th% |
75th% |
90th% |
95th% |
|---|---|---|---|---|---|---|---|
|
0 |
32.1 |
32.9 |
33.5 |
34.3 |
34.8 |
35.5 |
35.9 |
|
1 |
34.2 |
34.8 |
35.6 |
36.4 |
37.1 |
37.8 |
38.3 |
|
3 |
37.3 |
37.8 |
38.7 |
39.5 |
40.4 |
41.2 |
41.7 |
|
6 |
40.3 |
40.9 |
41.6 |
42.4 |
43.3 |
44.1 |
44.6 |
|
9 |
42.3 |
42.8 |
43.5 |
44.3 |
45.1 |
46 |
46.4 |
|
12 |
43.5 |
44.1 |
44.8 |
45.6 |
46.4 |
47.2 |
47.6 |
|
18 |
45 |
45.6 |
46.3 |
47.1 |
47.9 |
48.6 |
49.1 |
|
24 |
46.1 |
46.5 |
47.3 |
48.1 |
48.8 |
49.6 |
50.1 |
|
30 |
47 |
47.3 |
48 |
48.8 |
49.4 |
50.3 |
50.8 |
|
36 |
47.6 |
47.9 |
48.5 |
49.3 |
50 |
50.8 |
51.4 |
Polynomial equations approximating this data were calculated in JMP, as follows:
5th% for head circumference in centimeters =
= ((0.0000012 * ((months)^5)) - (0.000148 * ((months)^4)) + (0.0069556 * ((months)^3)) - (0.163182 * ((months)^2)) + (2.1303285 * (months)) + 32.158424)
10th% for head circumference in centimeters =
= ((0.0000009 * ((months)^5)) - (0.000112 * ((months)^4)) + (0.0055756 * ((months)^3)) - (0.141338 * ((months)^2)) + (1.9989488 * (months)) + 32.919519)
25th% for head circumference in centimeters =
= ((0.0000015 * ((months)^5)) - (0.000173 * ((months)^4)) + (0.007584 * ((months)^3)) - (0.168351 * ((months)^2)) + (2.1255298 * (months)) + 33.56967)
50th% for head circumference in centimeters =
= ((0.0000015 * ((months)^5)) - (0.000173 * ((months)^4)) + (0.007584 * ((months)^3)) - (0.168351 * ((months)^2)) + (2.1255298 * (months)) + 34.36967)
75th% for head circumference in centimeters =
= ((0.0000022 * ((months)^5)) - (0.000238 * ((months)^4)) + (0.0097861 * ((months)^3)) - (0.200918 * ((months)^2)) + (2.319393 * (months)) + 34.892429)
90th% for head circumference in centimeters =
= ((0.000002 * ((months)^5)) - (0.000225 * ((months)^4)) + (0.0095797 * ((months)^3)) - (0.202581 * ((months)^2)) + (2.3600106 * (months)) + 35.57647)
95th% for head circumference in centimeters =
= ((0.0000025 * ((months)^5)) - (0.000263 * ((months)^4)) + (0.0107852 * ((months)^3)) - (0.217873 * ((months)^2)) + (2.4261526 * (months)) + 35.996165)
Distribution of Head Circumference by Month
If the same data is analyzed for each month, then the percentile represented by a given head circumference 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.
5 to 50%ile
|
age in years |
head^2 |
head |
coefficient |
|---|---|---|---|
|
0 |
8.9285714 |
-572.0879 |
9168.5865 |
|
0.08 |
7.6595745 |
-520.3319 |
8841.4340 |
|
0.25 |
7.2460114 |
-536.2795 |
9927.2723 |
|
0.5 |
8.0084129 |
-640.704 |
12818.7820 |
|
0.75 |
7.6161563 |
-636.9205 |
13319.0420 |
|
1 |
8.0084129 |
-691.9579 |
14951.0410 |
|
1.5 |
8.0084129 |
-715.9831 |
16006.9970 |
|
2 |
7.0665829 |
-643.3103 |
14643.8330 |
|
2.5 |
6.1605449 |
-565.2556 |
12963.4800 |
|
3 |
5.5454984 |
-510.7165 |
11750.1020 |
51 to 95%ile
|
age in years |
head^2 |
head |
coefficient |
|---|---|---|---|
|
0 |
-17.150840 |
1231.30750 |
-22005.50 |
|
0.08 |
-9.934896 |
765.78808 |
-14661.32 |
|
0.25 |
-5.769429 |
489.00749 |
-10264.09 |
|
0.5 |
-5.769429 |
522.47018 |
-11730.74 |
|
0.75 |
-7.072285 |
662.56164 |
-15422.00 |
|
1 |
-7.066583 |
680.96734 |
-16308.07 |
|
1.5 |
-7.616156 |
755.31283 |
-18629.57 |
|
2 |
-9.516090 |
956.71999 |
-23951.51 |
|
2.5 |
-11.462920 |
1163.41390 |
-29425.64 |
|
3 |
-9.564570 |
984.36147 |
-25232.23 |
