Statistics deals with the collection, analysis, and presentation of numerical data by way of mathematical theories. If valid, this information is used to help various agencies, industries, and researchers determine the best ways to produce results in their work. This data is then examined and determined to be reliable and useful or invalid. In order to make valid interpretations possible, statisticians advise on sampling techniques, data collection methods, survey design/methodology, and methods of data analysis. Theories such as probability and inference are examined to discover the mathematical bases for new and/or improved methods of obtaining and evaluating numerical data.