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In this work, we have considered the flat FRW model of the universe in$(n+2)$-dimensions filled with the dark matter (perfect fluid with negligiblepressure) and the modified Chaplygin gas (MCG) type dark energy. We present theHubble parameter in terms of the observable parameters $\Omega_{m0}$,$\Omega_{x0}$ and $H_{0}$ with the redshift $z$ and the other parameters like$A$, $B$, $C$, $n$ and $\alpha$. From Stern data set (12 points), we haveobtained the bounds of the arbitrary parameters by minimizing the $\chi^{2}$test. The best-fit values of the parameters are obtained by 66%, 90% and 99%confidence levels. Now to find the bounds of the parameters and to draw thestatistical confidence contour, we first fixed three parameters $C, n, \alpha$and then fixed the three parameters $A, n, \alpha$. In the first case we findthe bounds of $(A, B)$ and draw the contour between them for 4D$(n=2)$,5D$(n=3)$ and 6D$(n=4)$. In the second case we fixed three different values ofA as 1, 1/3, -1/3 to find the bounds of $(B, C)$ and draw the contour betweenthem. Here the parameter $n$ determines the higher dimensions and we performcomparative study between three cases : 4D $(n=2)$, 5D $(n=3)$ and 6D $(n=4)$respectively. Next due to joint analysis with BAO observation, we have alsoobtained the bounds of the parameters ($A,B$) by fixing some other parameters$\alpha$ and $A$ for 4D, 5D and 6D.

Observational Constraints of Homogeneous Higher Dimensional Cosmology with Modified Chaplygin Gas