This chapter reviews the basic concepts of the statistics of measurements and provides guidance in their application. Statistical principles are applied when demonstrating statistical control, evaluating data, designing measurement and sampling plans, and making a wide variety of decisions in the use and application of measurements. The results of repetitive measurements are usually considered to be normally distributed and representable by a bell-shaped curve. As an example, replicate measurements may be made on a number of samples randomly selected from a material of interest. The standard deviation may be estimated from the differences of several sets of duplicate measurements. These may be duplicate measurements of the same sample on several occasions, or they may be duplicate measurements of different samples. In many measurement situations, the total variance may be considered to arise essentially from two major sources, such as that of the measurement process and that of the samples measured.