JoinMean = Join[{MeanC5cm, MeanC7cm, MeanC10cm, MeanC20cm, MeanC27cm, MeanC30cm}]
{44.0215, 73.6246, 117.757, 307.112, 445.527, 352.733}

JoinStDv = Join[{Sd5, Sd7, Sd10, Sd20, Sd27, Sd30}]
{3.31495, 3.27642, 23.9473, 27.6356, 25.0707, 23.2319}

Graph1 = ErrorListPlot[{{{5, MeanC5cm},
ErrorBar[Sd5]}, {{7, MeanC7cm}, ErrorBar[Sd7]}, {{10, MeanC10cm},
ErrorBar[Sd10]}, {{20, MeanC20cm},
ErrorBar[Sd20]}, {{27, MeanC27cm},
ErrorBar[Sd27]}, {{30, MeanC30cm}, ErrorBar[Sd30]}},
AxesOrigin -> {0, 0}, AxesLabel -> {"Length", "K\[CapitalOmega]"}]

MeanGradient = Fit[JoinMean, {1, x}, x]
-61.3992 + 81.389 x


MeanGradient =  Fit[Transpose[{{5, 7, 10, 20, 27, 30}, JoinMean}], {1, x}, x];

Show[Graph1, Plot[MeanGradient, {x, 0, 30}, PlotStyle -> Directive[Red, Thick]],
PlotRange -> All, PlotLabel -> MeanGradient]


Alternatively, you can add the option

Epilog -> Plot[MeanGradient, {x, 0, 30}, PlotStyle -> Directive[Red, Thick]][[1]]


to your ErrorListPlot that produces Graph1.

• Thank you i will give it a try.
– ljsg
Commented Jun 27, 2018 at 6:06