Summary
Highlights
Descriptive statistics describe and summarize data meaningfully, providing a simple overview of main characteristics. Importantly, they only describe collected data without drawing conclusions about a larger population. This role belongs to inferential statistics.
These measures include mean, median, and mode. The mean is the sum of observations divided by their number. The median is the middle value in an ordered dataset, resistant to extreme values. The mode is the most frequently appearing value(s) in a dataset, which can be unimodal, bimodal, multimodal, or even non-existent.
Measures of dispersion describe how spread out data values are. Examples include standard deviation, variance, range, and interquartile range. Standard deviation indicates the average distance of each data point from the mean. Variance is the squared standard deviation. The range is the difference between the minimum and maximum values, while the interquartile range represents the middle 50% of the data.
Measures of central tendency provide a single representative value for the dataset, indicating where data points cluster. Measures of dispersion show how spread out the data points are around that center, indicating whether they are closely packed or widely distributed.
Frequency tables display how often each distinct value appears in a dataset. Contingency tables (cross-tabs) are used when there are two categorical variables, showing the number of observations for each combination of categories.
Common charts for descriptive statistics include bar charts and pie charts for categorical data. Grouped or stacked bar charts can be used for two categorical variables. For numerical and categorical data, bar charts can show mean values and dispersion. Histograms, box plots, violin plots, and rainbow plots are also useful for visualizing data distribution.