  Some prominent discretisation methods such as finite elements provide a way
to approximate a function of $d$ variables from $n$ values it takes on the
nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in
$L^2$-norm, where $s_a$ is the order of the underlying method. When the data
are measured or computed with systematical experimental noise, some statistical
regularisation might be desirable, with a smoothing method of order $s_r$ (like
the number of vanishing moments of a kernel). This idea is behind the use of
some regularised discretisation methods, whose approximation properties are the
subject of this paper. We decipher the interplay of $s_a$ and $s_r$ for
reconstructing a smooth function on regular bounded domains from $n$
measurements with noise of order $\sigma$. We establish that for certain
regimes with small noise $\sigma$ depending on $n$, when $s_a > s_r$,
statistical smoothing is not necessarily the best option and {\it not
regularising} is more beneficial than {\it statistical regularising}. We
precisely quantify this phenomenon and show that the gain can achieve a
multiplicative order $n^{(s_a-s_r)/(2s_r+d)}$. We illustrate our estimates by
numerical experiments conducted in dimension $d=1$ with $\mathbb P_1$ and
$\mathbb P_2$ finite elements.
