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# 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:

- O
^{th}percentile or sample minimum: the smallest observation. - 25
^{th}percentile or first quartile or upper quartile. - 50
^{th}percentile or median. - 75
^{th}percentile or third quartile or upper quartile. - 100
^{th}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 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.

###### Additional References

- Glen, S. (2013).
*How to find a 5 number summary*. Available athttps://www.youtube.com/watch?v=omOSu7_Z22o