Describing Distributions of Populations from Samples

For any given characteristic of a population that we wish to measure, there is a distribution of measurements in the sample that we actually observe and see. But the measurements in the sample are only estimates or approximations of the measurements of the whole population. The measurements of population have a distribution as well, but this is usually not observable (unless the whole population can be measured). For example, we may be interested in knowing the average body weight of a certain species of spider. It is virtually impossible to capture and weigh every spider in a biological population. It is possible, however to take a sample of 300 spiders and weigh them. These weights (or measurements) have a particular distribution - that is, a plot of weight on the x-axis against the number of individuals found to have that weight on the y-axis has a particular shape. The question of interest then becomes: how closely does this sample distribution match the real distribution of the entire population of spider weight. As previously stated, one of the most important problems in statistics is to decide what information about the distribution of the population can be inferred from a study of the distribution of the sample.