clear
clf

% Uniform distribution
a = rand(10,1)
hist(a)

% Uniform distribution
a = rand(10000,1);
hist(a)
std(a)

% Normal distribution
b = randn(10000,1);
hist(b)
std(b)

% which one varies more about the mean?
b1 = randn(1000000,1)/2;
b2 = randn(1000000,1)*2;

hist( [b1 - 5 ; b2 + 5], 100 )
[var(b1) var(b2)]
sqrt([var(b1) var(b2)])
[std(b1) std(b2)]

clear

% perfect surface
a = zeros(100);
% for convenience
a = a(:);
[mean(a) (max(a) - min(a)) std(a)]

b = a;
b(1) = 0.25;
[mean(b) (max(b) - min(b)) std(b)]

% make b twice as good
b = b/2;
[mean(b) (max(b) - min(b)) std(b)]

% make a uniformly random surface with same PV as b
c = rand(size(b));
c = c - min(c);
c = c * (max(b) - min(b))/(max(c));
[mean(c) (max(c) - min(c)) std(c)]

% Same PV - vastly different rms (std) values - which would you want?