Trimmed mean, introduced by Tukey (1948), has been extensively studied in the literature as an estimate of the location parameter. It is well-known for being more robust and for having better mean square error than the usual mean when data arise from non-Gaussian distributions with heavy tails. In this paper, we consider the derivatives of trimmed mean with respect to the trimming proportion and investigate some statistical applications of those derivatives. We develop a diagnostic tool based on the first derivative of trimmed mean to determine whether the data is generated from a symmetric distribution or not. We also propose a test of symmetry of the distribution based on the first derivative and demonstrate that it performs better than several other well-known tests of symmetry studied by earlier authors. Further, we introduce an estimate of the contamination proportion β ∈ (0, 1/2) in the contamination model F (x) = (1−β)H(x)+βG(x), where H and G are two distributions such that G is stochastically larger than H, based on the second derivative of the trimmed mean. In addition to some theoretical studies, we carry out a detailed numerical study to show that, in many situations, our proposed estimate of the contamination proportion outperforms other estimates, which are based on the idea of maximum likelihood estimation in mixture models.