In this paper, we consider precoder design for wireless data aggregation in sensor networks. The precoder optimization problem can be formulated as minimization of mean squared error under transmit power and block diagonal constraints. We include statistical correlation of data into the optimization problem, which is appeared in typical applications but is ignored in conventional designing methods. We propose precoder optimization algorithms based on projected gradient descent with projection onto the constraint sets. The proposed method can achieve better performance than the conventional methods that do not incorporate data correlation, especially when data are highly correlated. We also extend the proposed approach to the context of over-the-air computation.