A Five Number Summary is a statistical tool that describes the distribution of a dataset through five key values: the minimum value, the first quartile (Q1), the median (Q2 or the 50th percentile), the third quartile (Q3), and the maximum value.

These points divide the dataset into four equal parts and provide a quick overview of its spread, central tendency, and potential outliers, facilitating comparisons between different datasets and serving as a foundation for creating box-and-whisker plots.

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Check out other useful tools in Statistics & Mathematics - RREF Calculator & Interpolation Calculator.

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The Five Number Summary is used to provide a concise description of a dataset's distribution, offering insights into its central tendency, variability, and shape. By including the minimum, first quartile, median, third quartile, and maximum, it helps in identifying outliers, understanding data spread, and facilitating comparisons between datasets, making it valuable for statistical analysis and data visualization, such as in box-and-whisker plots.

How to Calculate the Five-Number Summary by hand?

​To calculate the five-number summary by hand:

​1. Sort the data from smallest to largest.
2. Find the minimum and maximum values.
3. Calculate the median (Q2): For an odd number of data points, it's the middle value. For an even number, it's the average of the two middle values.
4. Determine Q1 and Q3: Q1 is the median of the data points to the left of the overall median, and Q3 is the median of the data points to the right.

Example: For the dataset 1, 2, 3, 4, 5, 6, 7, 8, 9:
​Minimum: 1
Q1: 3 (median of 1, 2, 3, 4)
Median (Q2): 5
Q3: 7 (median of 6, 7, 8, 9)
Maximum: 9
This method gives a snapshot of the dataset's distribution.