% Matlab demonstration of how a density curve can be used to estimate
%   a distribution of data.

% draw 10000 height samples from male population
mu=68.5;sigma=5.5;n=10000;
test_value=64;
X=normrnd(mu,sigma,n,1);
% vector for density curve
x=[45:0.01:95];
y=normpdf(x,mu,sigma);
figure(1);clf;
subplot(2,1,1);
title('Using a density curve to approximate a data distribution, N(68.5,5.5).');
xlabel('Heights of 10000 men in inches.');
ylabel('Proportion of men at each height.');
% plot histogram of sample
binwidth=2;
bins=[41:binwidth:89];
N=hist(X,bins);hold on;
N=N/(n*binwidth);
bar(bins,N,1);
% plot density curve
plot(x,y,'r');
axis([45 95 0 0.08]);

% find area to the left of test_value
less_hist=find(X<test_value);
prop_hist=length(less_hist)/n;
prop_dist=normcdf(test_value,mu,sigma);

subplot(2,1,2);
% plot density curve
x_test_value=[45:0.01:test_value];
y_test_value=normpdf(x_test_value,mu,sigma);
area(x_test_value,y_test_value);

% plot histogram of the select sample
N=hist(X(less_hist),bins);hold on;
N=N/(n*binwidth);
bar(bins,N,1);
axis([45 95 0 0.08]);

text(65,.035,strcat('Proportion of men shorter than ',num2str(test_value),' inches:'))
text(65,.03 ,strcat('  Histogram: ', num2str(prop_hist)))
text(65,.025,strcat('  Density:   ', num2str(prop_dist)))


% eof