Physical meaning of coefficient of variation While doing a course in statistical physics I came across a term called coefficient of variation. Now according to Wikipedia, coefficient of variation

shows the extent of variability in relation to mean of the population

However I don't see the connection to physics in this. For example considering nuclear decay, what is the physical meaning of coefficient of variation in this process?
 A: Suppose you have some radioactive material with a half life $\tau_{1/2}$. What that term "half life" means is that the amount of material $m(t)$ you have left after a time $t$ is
$$m(t) = m(0) \exp[ -t / \tau_{1/2}] . \qquad (*)$$
However, the material is made up of discrete atoms and each one decays in a random way.
Therefore, it's not 100% guaranteed that after a time $\tau_{1/2}$ there is exactly half as much material left.
It could be a bit more or a bit less.
In other words, on any particular trial equation $(*)$ will not necessarily be satisfied.
Equation $(*)$ tells you the average amount of material left over.
It means basically this:

Get a large number $N$ of independent lumps of material with initial mass $m_i(0)$. Wait a time $\tau_{1/2}$. The resulting $m_i(\tau_{1/2})$ values are random but with a probability distribution whose mean $\mu$ is given by $(*)$.

Since the remaining amount of material is given by a probability distribution you can ask for more than just it's mean value.
In particular, you could ask for the entire distribution, i.e. the probability of finding any particular remaining amount of material after a time $t$.
This might be denoted $P(m|m(0),t)$, i.e. "The probability of having an mount m left over, given that started with an amount $m(0)$ and am now looking at time $t$ later".
Anyway, one useful property of a probability distribution is its width $\sigma$, also called the "standard deviation".
The coefficient of variation is defined as $c \equiv \sigma/\mu$.
This just answers the question "how wide is my distribution as compared to its mean?"
It's a useful quantity because it allows you to easily relate the variability of the process to the mean behavior.
In other words, it tells you how predictable the process really is, i.e. how closely it sticks to its average behavior.
Example: random walk
On each step either I either move one space to the right or I stand still, with 1/2 probability of each.
You may have learned that the probability distribution for my position after $N$ steps is a binomial distribution.
The mean $\mu$ is simply $\mu = N/2$ because I have a 1/2 chance of progressing on each step.
You can see that, in a sense, my position becomes more uncertain as time goes on because my $\sigma$ increases with $N$.
However, the variability of my position compared to my mean position is actually going down because $\sigma/\mu \propto 1/\sqrt{N}$.
Intuitively this is saying that while the variability is going up, it's mattering less as compared to the scale of the problem.
It's like saying that a 1 mile uncertainty in the distance from you to the sun is actually a lot less important than a 1 centimeter uncertainty in the distance between two atoms.
I brought up the random walk example because it comes up all over experimental physics.
If you integrate a signal longer you actually get more noise ($\propto \sqrt{t}$), but you get more signal faster ($\propto t$) than you get more noise, so the signal to noise ratio ($\propto \sqrt{t}$) gets better.
