In various fields of life, precise estimation of a finite population’s mean is required. The conventional ratio estimators can only work with precisely defined observations. These conventional estimators may give misleading results in real life situations in which some, if not all, data points are inevitably vague, indeterminate or imprecise. Using probability proportional to size sampling, we present an enhanced neutron-sophic mean estimator utilizing an ancillary variable. The suggested neutron-sophic estimator has been designed to handle imprecise measurements in data sets. We assess various statistical properties of our suggested neutron-sophic estimator. Our results indicate that the new ratio estimator improves the efficiency of the competitor ratio estimators in the presence of imprecise measurements. We use real-life neutron-sophic data to show the improvement under unequal probability sampling.