In hadronic decays of Z$^0$ bosons recorded with the OPAL detector at
LEP, events containing b quarks were selected using the long lifetime of
b flavoured hadrons. Comparing the $3$-jet rate in b 
events with that in d,u,s and c quark events, a significant difference
was observed.
Using ${\cal O}(\alpha_{\mathrm s}^2)$ calculations for massive quarks, this
difference was used to determine the b quark mass in the
$\overline{\mathrm{MS}}$ 
renormalisation scheme at the scale of the Z boson mass. By
combining the results from seven different jet finders
the running b quark mass was determined to be
$${\overline {\mathrm m}}_{\mathrm b}({\mathrm m}_{\mathrm Z}) = 
2.67 \pm 0.03~{\mathrm {(stat.)}}~^{+0.29}_{-0.37}~{\mathrm {(syst.)}}
~\pm 0.19~({\mathrm {(theo.)}}~{\mathrm {GeV.}}$$
Evolving this value to the b quark mass scale itself
yields 
${\overline {\mathrm m}}_{\mathrm b}({\mathrm m}_{\mathrm b}) =
3.95~^{+0.52}_{-0.62}$~GeV,
consistent with results obtained at the b quark production
threshold. This determination confirms the QCD expectation of a scale
dependent quark mass. A constant mass is ruled out by 3.9 standard
deviations.