Question

This table gives body mass index (BMI) as a function of age and percentile of the population.

Age/Percentile	10%	20%	30%	40%	50%	60%	70%	80%	90%
10 Years	14.9	15.6	15.8	16.6	17	18.7	19.3	19.9	20.3
20 Years	19.7	20.4	21.2	22	22.5	23.8	25.4	26.9	28.4
30 Years	20.8	21.9	22.8	23.9	25	26.4	28.1	29.5	32.3
40 Years	22.7	23.3	24.1	25.5	26.5	28	29.2	31	33.5
50 Years	23	23.7	24.7	25.8	26.75	28.2	29.9	31.3	33.9
60 Years	22.9	23.8	24.6	25.9	27	28.3	29.8	31.2	33.8
70 Years	22.7	23.7	24.5	25.7	26.75	28.1	29.4	31	32.3

Interpolate to find the BMI for the 75% percentile of 67 year-olds (use linear, cubic and spline), give the value for each method to 1 decimal place using Matlab.

Answer 1

Below is the code for performing the interpolation of scattered data. For performing the interpolation, the function used here is griddata(). It supports the methods 'linear' and 'cubic'. Since 'cubic' is a class of spline function, it gives the same result as spline method and hence is not written exclusively in the code.

% Defining age matrix
age = linspace(10,70,7);
age = repmat(age,9,1);

% Defining percentile matrix
percentile = linspace(10,90,9);
percentile = repmat(percentile,7,1)';

% Defining BMI data matrix
bmi = [
14.9, 19.7, 20.8, 22.7, 23, 22.9, 22.7;
15.6, 20.4, 21.9, 23.3, 23.7, 23.8, 23.7;
15.8, 21.2, 22.8, 24.1, 24.7, 24.6, 24.5;
16.6, 22, 23.9, 25.5, 25.8, 25.9, 25.7;
17, 22.5, 25, 26.5, 26.75, 27, 26.75;
18.7, 23.8, 26.4, 28, 28.2, 28.3, 28.1;
19.3, 25.4, 28.1, 29.3, 29.9, 29.8, 29.4;
19.9, 26.9, 29.5, 31, 31.3, 31.2, 31;
20.3, 28.4, 32.3, 33.5, 33.9, 33.8, 32.3
]

% Linear interpolation
griddata(percentile,age,bmi,75,67)

% Cubic interpolation
griddata(percentile,age,bmi,75,67,'cubic')

After evaluating the code in MATLAB, the answer obtained for BMI in the 75% percentile for 67 years of age is:

• Linear order: 30.32
• Cubic order/ Spline: 30.24

Please note that the values fluctuate every time the code is evaluated since the algorithm used for griddata always starts with random initial assumptions. However after convergence towards the solution, its value will lie very close to the above mentioned values.