Is the refractive index of a solution of four substances the median of the four substances' refractive index?
There is no single equation that accurately predicts the refractive index of a mixture.  This reference discusses 9 approaches to estimating the refractive index of mixtures and provides the formula for each method. The simplest method is the Arago-Biot approach.  It is reasonably reliable and is described by the following formula

$$n = n_1 \phi_1 + n_2\phi_2$$

where $n$ is the predicted refractive index of the mixture, $n_x$ is the refractive index of the $x^{th}$ component, and $\phi_x$ is the volume fraction of the $x^{th}$ component.  The volume fraction of the first component is given by

$$\phi_1 = x_1 V_1 / \Sigma~ x_i V_i$$
Here $x_i$ is the mole fraction of the $i^{th}$ component and $V_i$ is the molar volume (the molecular weight divided by the density) of the $i^{th}$ component. The more ideal the liquids, the more accurate the predictions.