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https://en.wikipedia.org/wiki/Toluidine

In m-toluidine the $\ce{CH3}$ group is closer to $\ce{N}$ so shouldn't that increase the electron density on $\ce{N}$ and make it a stronger base?

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In p-toluidine you are not actually considering the hyper conjugating structures due to which the compound becomes more basic than m-toluidine which only has it's +I effect and I would like to suggest you that as far as I know resonance effect "usually" overpowers the other effect!

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