Populations

If statistics is the organization, analysis and presentation of numerical observations or measurements of data, then we need to understand how we collect and define our data. Let's start with the largest set of data. A population is defined as all possible data values for a given measurement. For example, if we were to collect exhaust measurements from every car in the United States, then we would have collected measurements for the U.S. vehicle population. The same is true if we could collect the ozone concentration in the troposphere every second of every day. In essence, we would be collecting the population of ozone concentration measurements. In both situations, the collection of data is a major challenge. Usually it is impossible or impractical to examine every measurement in a population. In cases such as ozone concentrations in the troposphere, it is unlikely that we would be able to make sense of so many measurements even if we could collect them all.

Samples

Scientists overcome these obstacle be collecting a smaller number of data values called a sample. The word "sample" means a small subset of a much larger set of data. Samples are created by collecting a random selection of data values. Random samples are good representations of populations. By performing statistical procedures on a sample, scientists can draw conclusions about the whole population. For example, if the average value of a randomly selected sample of tropospheric data were 0.50 ppm ozone, then we could assume that this is a good estimate of all the possible ozone measurements in the population.