Several simple estimates of the mean and standard deviation of a normal population are discussed. The efficiencies of these estimates are compared to the sample mean and sample standard deviation and to the best linear unbiased estimates. Little efficiency is lost when simple rather than optimum weights are used. Since moments of the order statistics are now available for samples of sizes $N \leqq 20$ from normal populations  it is a simple matter to find the variances of linear combinations of order statistics. The sample values are denoted $X_1 \leqq X_2 \leqq X_3 \leqq \cdots \leqq X_N$.
"Estimates of the Mean and Standard Deviation of a Normal Population." Ann. Math. Statist. 28 (3) 806 - 809, September, 1957. https://doi.org/10.1214/aoms/1177706898