# Descriptive Statistics

The descriptive statistics feature of statistiXL provides a quick and easy summary of the basic parametric and nonparametric statistics that describe a sample of values. Unlike many packages, statistiXL provides modules for both linear data and circular descriptive statistics.

A sample of values collected using a linear scale (e.g. length, mass, temperature) can be described by a variety of descriptive statistics, the more common being the mean, median, variance and standard deviation. The descriptive statistics which can be provided (by user selection) with the linear descriptive statistics module are: mean, median, mode, standard error, standard deviation, variance, coefficient of variation, lower and upper confidence limits, 25th and 75th percentiles, sum, minimum and maximum values, nth smallest and largest values (with user input of n), range, count, skewness (with probability if count >9) and kurtosis (with probability if count >19).

If these data are sampled at random from a normal distribution, then the data are best summarized by the parametric statistics such as mean, variance and standard deviation. If the data are sampled from a non-normal distribution, then the non-parametric statistics such as median, mode, percentiles and range may be more appropriate statistics for summarizing these data. Options for graphical output includes a “box and whisker” plot and an error bar plot.

A sample of values collected using a circular scale (e.g. time of day or compass bearing) can be described by a variety of descriptive statistics, the more common being the mean angle, angular variance and angular standard deviation. The information provided in the circular descriptive statistics module is mean angle, angular standard deviation, angular variance, circular standard deviation, circular variance, lower and upper 95% confidence limits for the mean angle, and the count. Circular data can be examined for goodness-of-fit to a circular distribution using the Goodness-of-Fit module. Optional graphical output includes a circular plot.

In addition to the Linear and Circular Descriptive Statistics modules statistiXL also provides a module for analysing freqency distributions for norminal and numerical data. Data can be entered either as raw observations or pre-determined freqency tables. Output will include counts, cumulative counts, percentages and cumulative percentages for each category. Histograms of the counts can also be produced.

The help file included with statistiXL provides an overview of descriptive statistics, and examples of linear, circular and frequency based descriptive statistical analysis.