  Let $G$ be a connected edge-weighted graph of order $n$ and size $m$. Let
$w:E(G)\rightarrow \mathbb{R}^{\geq 0}$ be the weighting function. We assume
that $w$ is normalised, that is, $\sum_{e\in E(G)} w(e)=m$. The weighted
distance $d_w(u,v)$ between any two vertices $u$ and $v$ is the least weight
between them and the eccentricity $e_w(v)$ of a vertex $v$ is the weighted
distance from $v$ to a vertex farthest from it in $G$. The mean(average)
eccentricity of $G$, $avec(G,w)$, is the (weighted) mean of all eccentricities
in $G$. We obtain upper and lower bounds on $avec(G,w)$ in terms of $n$, $m$ or
edge-connectivity $\lambda$ for two cases: $G$ is a tree and $G$ is connected
but not a tree. In addition, we obtain the Nordhaus-Gaddum-type results for
edge-weighted average eccentricity.
