*expect*young mechanics to move mountains.

Any measurement of a particle presumably involves some sort of interaction that changes its quark content. The change may be small, maybe even negligible, but nonetheless there is always a logical distinction between an observed value and the theoretical concept of the energy of an isolated particle. The customary way of assessing this fuzziness is to make many observations, so consider a series of $N$ measurements with results noted by $E^{1}, \, E^{2}, \, E^{3} \ \ldots \ E^{\it{k}} \ \ldots \ E^{\it{N}}$. These observed values are related to $E$ the theoretical idea of energy by

$E = \tilde{E} \pm \delta E$

where $\tilde{E}$ is a typical or representative value called the**experimental average**. The other number $\delta E$ describes the variation in observed values, it is called the

**experimental uncertainty**. For 'good' measurements $\delta E$ is small enough so that $E$ and $\tilde{E}$ are interchangeable thus reconciling theory and observation. Usually the experimental average is determined from the arithmetic mean of the set of observations

$\tilde{E} = \frac{1}{ N} \sum_{k=1}^{N} \; E^{k}$

and the experimental uncertainty is represented by their standard deviation$\delta E = \sqrt{ \frac{1}{N} \sum_{k=1}^{N} \left( E ^{k} - \tilde{E} \right)^{2} \ }$

Another important number is the coefficient of variation in the data which is defined by the ratio $\delta E / \tilde{E}$. The inverse of this quantity is known as the signal-to-noise ratio$\varsigma = 10 \log{ \left(\tilde{E} / \delta E \right) }$ (dB)

expressed on a logarithmic scale in units of decibels.