The statistical behaviours of the variance, covariance and gradients of reaction progress variable c, and mixture fraction xi have been analysed in an ethanol turbulent spray jet flame based on the results obtained from a carrier-phase three-dimensional Direct Numerical Simulation (DNS) dataset. It has been observed that the Favre Probability Density Functions (PDFs) of c and xi extracted from the DNS data are correctly estimated by a standard beta-PDF. Furthermore, the log-normal distribution has been found to accurately represent vertical bar del xi vertical bar, but small discrepancies were found at the head of the distribution. By contrast,vertical bar del c vertical bar was found to be only marginally represented by a log-normal distribution with non-negligible departures from the DNS data at both the head and the tail of the distribution. It has also been found that del c and del xi show predominant collinear alignment throughout the flame brush. Finally, the joint-PDF vertical bar del c vertical bar and vertical bar del xi vertical bar, (i.e. P (vertical bar del c vertical bar X vertical bar del xi vertical bar)) has been compared with the product of the marginal PDFs vertical bar del c vertical bar and vertical bar del xi vertical bar (i.e. P (vertical bar del c vertical bar) x P (vertical bar del xi vertical bar)) extracted from DNS (i.e. assuming statistical independence) and a good agreement has been observed. The bivariate log-normal distributions with and without correlation have also been considered and fail to capture the DNS trend, which stems from the difficulties of approximating P (vertical bar del c vertical bar) and P (vertical bar del xi vertical bar) with log-normal PDFs.