Classical statistical estimators are limited by their reliance on deterministic data, making them ineffective when observations are imprecise or indeterminate. Neutrosophic statistics overcome this issue by giving observations in the form \({Z}_{N}=a+bI\) with ‘a’ denoting the determinate component and ‘bI’ representing the indeterminate component. In this paper, we present a novel neutrosophic estimator for estimating population mean under indeterminacy. The bias and mean squared error equations for the proposed estimator are derived up to first-order Taylor series, and its efficiency is compared with current classical and neutrosophic estimators. Theoretical features of the estimator are determined by applying standard, large-sample approximations inside the neutrosophic framework. Furthermore, efficiency requirements are defined to identify instances in which the suggested estimator outperforms the competing estimators examined in this work. The proposed estimator’s performance is evaluated using Monte Carlo simulations and three real-world case studies involving medical diagnostics (estimation of body temperature using blood pressure data in gastroenterology), network traffic analysis, and longitudinal sales data collected during the COVID-19 pandemic. The results show that, for the investigated populations and simulation settings, the suggested estimator achieves lower mean squared error and a greater percentage relative efficiency than the competing estimators considered in this study.
