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In the Friedmann cosmology the deceleration of the expansion $q$ plays afundamental role. We derive the deceleration as a function of redshift $q(z)$in two scenarios: $\Lambda$CDM model and modified Chaplygin gas ($MCG$) model.The function for the $MCG$ model is then fitted to the cosmological data inorder to obtain the cosmological parameters that minimize $\chi^2$. We use theFisher matrix to construct the covariance matrix of our parameters andreconstruct the q(z) function. We use Supernovae Ia, WMAP5 and BAO measurementsto obtain the observational constraints. We determined the present accelerationas $q_0=-0.60 \pm 0.12$ for the $MCG$ model using the Constitution dataset ofSNeIa and BAO, and $q_0=-0.63 \pm 0.17$ for the Union dataset and BAO. Thetransition redshift from deceleration to acceleration was found to be around$0.6$ for both datasets. We have also determined the dark energy parameter forthe $MCG$ model: $\Omega_{X0}=0.834 \pm 0.028$ for the Constitution dataset and$\Omega_{X0}=0.854 \pm 0.036$ using the Union dataset.

Fitting cosmological data to the function $q(z)$ from GR Theory: Modified Chaplygin Gas