A measure of possibilistic correlation between marginal possibility distributions of a joint possibility distribution can be defined as (see Fullér, Mezei and Várlaki, An improved index of interactivity for fuzzy numbers, Fuzzy Sets and Systems, 165(2011), pp. 56-66) the weighted average of probabilistic correlations between marginal probability distributions whose joint probability distribution is defined to be uniform on the level sets of their joint possibility distribution. Using the averaging technique we shall discuss three quantities (correlation coefficient, correlation ratio and informational coefficient of correlation) which are used to measure the strength of dependence between two possibility distributions. We discuss the inverse problem, as we introduce a method to construct a joint possibility distribution for a given value of possibilistic correlation coefficient. We also discuss a special case when the joint possibility distribution is defined by the so-called weak t-norm and based on these results, we make a conjecture as an open problem for the range of the possibilistic correlation coefficient of any t-norm based joint distribution.