= Solution
Assuming independent Gaussian <measurement errors> with the quoted <standard deviations>, use the <inverse-variance weighted mean>:
$$
w_i=\sigma_i^{-2},\qquad
\bar x_w=\frac{\sum_iw_ix_i}{\sum_iw_i},\qquad
\sigma_{\bar x_w}=(\sum_iw_i)^{-1/2}.
$$
Here $\sum_iw_i=0.654514$ and $\sum_iw_ix_i=65.805556$, giving
$$
\boxed{\bar x_w=100.54\pm1.24}.
$$
The consistency statistic is $\chi^2=4.45$ for four <degrees of freedom>, so there is no evident excess scatter requiring error rescaling. A shared <systematic error> would require a <covariance matrix> and would not be reduced by this averaging rule.
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