Statistical properties of light waves reflected from a one-dimensional (1D) disordered optical medium [n(x) = n(0) + dn(x),= 0] have been well studied, however, most of the studies have focused on the situation when the mean refractive index of the optical medium matched with the outside medium, i.e., n(0) = n(out) = 1. Further, considering dn(x) as a Gaussian color noise refractive index medium with exponential spatial correlation decay length le and k as the incident wave vector, it has been shown that for smaller correlation length limit, i.e., kl(c) < < 1, both the mean reflection coefficientand std of r, sigma(r), have same value, and they follow the relation= sigma(r) proportional tol(c). However, when the refractive index of the sample medium is different from the outside medium, the reflection statistics may have interesting features, which has not been well studied or understood. We studied the reflection statistics of a 1D weakly disordered optical medium with the mean background refractive index no being different from the outside medium n(out) (not equal n(o)), to see the effect of mismatching (i.e., value of n(o) - n(out)) on the reflection statistics. In the mismatched case, the results show that the mean reflection coefficientfollows a form similar to that of the matched refractive-index case, i.e.,proportional tolc, with a linear increased shift, which is due to 1D uniform background reflection from a slab. However, sigma(r) is shown to be sigma(r) proportional to (l(c))(1/2), which is different from the matched case. This change in std of r is attributed to the interference between the mismatched-crerated edge mediated multiple scattering that are coupled with the random scattering. Applications to light scattering from random layered media and biological cells are discussed.