Statistics - explanations and formulas

Descriptive Statistics

Descriptive statistics are techniques used for describing, graphing, organizing and summarizing quantitative data. They describe something, either visually or statistically, about individual variables or the association among two or more variables. For instance, a social researcher may want to know how many people in his/her study are male or female, what the average age of the respondents is, or what the median income is. Researchers often need to know how closely their data represent the population from which it is drawn so that they can assess the data’s representativeness.

Descriptive statistics include mean, standard deviation, mode,and median.

Descriptive information gives researchers a general picture of their data, as opposed to an explanation for why certain variables may be associated with each other. Descriptive statistics are often contrasted with inferential statistics, which are used to make inferences, or to explain factors, about the population. Data can be summarized at the univariate level with visual pictures, such as graphs, histograms, and pie charts. Statistical techniques used to describe individual variables include frequencies, the mean, median, mode, cumulative percent, percentile, standard deviation, variance, and interquartile range. Data can also be summarized at the bivariate level. Measures of association between two variables include calculations of eta, gamma, lambda, Pearson’s r, Kendall’s tau, Spearman’s rho, and chi2, among others. Bivariate relationships can also be illustrated in visual graphs that describe the association between two variables.

(from Oxford Reference Online)