clear all

%%%%%%%%%%%%%%%%%%%%%%%
% Pie Chart:
% Ingrediants for a Sausage Mushroom Pizza weighing 1.6kg
% Sausage: 0.12kg
% Cheese: 0.4Kg
% Crust: 0.8Kg
% Tomato Sauce: 0.2Kg
% Mushrooms: 0.08Kg
% -------------------
% Pizza: 1.6Kg


pizza=[0.12 0.4 0.8 0.2 0.08];

figure;
pie(pizza,{'Sausage','Cheese','Crust','Tomato Sauce','Mushrooms'});
%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%
%%% For the histogram:
%%% Ask everyone in the room to tell me something about themselves realtime.
%%% Such as their heights (cm), age (year.month) etc.

nbins=70;
z=rand(300,1);

edg=min(z)+[0:1:nbins]*((max(z)-min(z))/nbins);
freq_z=histc(z,edg);
figure;
bar(edg,freq_z,'k')

%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%
%%% For the CLT, use a simulation study:

n=30;%number of observations
n_sims=1e4;%number of simulations

x=randn(n,n_sims);%matrix with pseudo-random values drawn from a normal distribution
                  %with mean zero and standard deviation onepseudo-random values
x_bar=mean(x);%vector of the mean values of every column in the matrix x

nbins=1e2;
v=x_bar;
edg=min(v)+[0:1:nbins]*((max(v)-min(v))/nbins);
freq_v=histc(v,edg);
%%%%
%% frequency histogram
%%%%

figure;
subplot(211)
bar(edg,freq_v,'b')
xlabel('Sample mean')
ylabel('Frequency')
%%%%
%% probability histogram
%%%%

% figure;
prob_v=freq_v/sum(freq_v);
subplot(212)
bar(edg,prob_v,'r')
xlabel('Sample mean')
ylabel('Probability')