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In this paper, we consider the Bianchi type-I space-time with perfect fluid as matter content of the Universe in the framework of $f(Q)$ gravity (where $% Q$ is the non-metricity scalar) recently proposed by Jim\'{e}nez et al. (Phys. Rev. D 98.4 (2018): 044048). We find exact solutions of the field equations using the anisotropic property of space-time for volumetric hybrid expansion. The cosmological parameters for the linear form of non-metricity scalar i.e. $f\left( Q\right) =\alpha Q+\beta $ (where $\alpha $ and $\beta $ are free model parameters) are discussed and compared with recent Hubble measurements. Also, we have obtained the best fitting values of the model parameters $k, n$ and $H_{0}$ by constraining our model with updated Hubble datasets consisting of 57 data points ($31$ (DA) and $26$ (BAO+other)) along with also examined the stability of the model and test its validity by energy conditions.