Statistics are mathematical techniques used to describe and draw inferences from quantitative data. Statistics are commonly divided into two branches: descriptive and inferential. Descriptive statistics are used to describe, summarize, and represent more concisely a set of data. Common descriptive statistics include frequency distributions, percentiles, the mean, and the range. Inferential statistics involve procedures for drawing inferences that go beyond the data set: conventionally, inferences about a large group (i.e., a population) based on observations of a smaller sample. Statistical inference could be used, for example, to estimate the relationship between variables (e.g., the correlation between income and amount of services received), to assess whether two groups differ (e.g., does the treatment group have better outcomes than the control group?), or to judge the fit ...