What is the Five Number Summary?
The five-number summary is a set of five statistics used to describe a dataset of quantitative data. These statistics are the five main percentiles:
- Oth percentile or sample minimum: the smallest observation.
- 25th percentile or first quartile or upper quartile.
- 50th percentile or median.
- 75th percentile or third quartile or upper quartile.
- 100th percentile or maximum: the largest observation.
All observations must be from a univariate variable that is measurable on an ordinal, interval, or ratio scale.
The five-number summary (5 number summary) is usually represented via a box plot. The different percentiles are indicated as follows: the minimum and the maximum with whiskers, the first and third quartile as the end of the rectangle, and the median with a line at the center of the rectangle. Outliers are symbolized with dots or asterisks.
Figure 1: five-number summary representation in a box plot
Why is the Five Number Summary Important?
A five-number summary is handy when dealing with a large amount of data, as it provides a concise overview of its distribution. In a single figure, the quartiles show information about the data spread, the median about location, and the maximum and minimum data range. Besides, the diagram can also include outliers, providing a very complete description of a dataset.
The five-number summary can also be used to compare different sets of observations and to evaluate intermediate L-estimators, such as the interquartile range, midhinge, range, mid-range, and trimean.
Five Number Summary and LogicPlum
LogicPlum platform’s main advantages are speed and accuracy. Additionally, LogicPlum helps users to analyze datasets, compare them, and organize them into better-structured data samples, all in an automated manner. Once the engine has found an optimal model, it provides a comprehensive explanation of the findings. Among the tools used in these tasks, five-number summaries provide a way to present clear pictures of the datasets involved, easily understood by experts and non-experts alike.