Five-Number Summary

five_number_summary(data, precision=4)

Calculates the five number summary of a given data set: minimum, first quartile, median, third quartile, and maximum

Parameters

  • data (list of int or float) – List of numbers to analyze

  • precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the result

Raises

  • TypeError – First argument must be a 1-dimensional list

  • TypeError – Elements of first argument must be integers or floats

  • ValueError – Last argument must be a positive integer

Returns

  • summary[‘minimum’] (float) – Smallest value from the data set

  • summary[‘q1’] (float) – First quartile of the data set, below which 25% of the data fall

  • summary[‘median’] (float) – Middle value of the data set, splitting the data evenly in half

  • summary[‘q3’] (float) – Third quartile of the data set, above which 25% of the data fall

  • summary[‘maximum’] (float) – Largest value from the data set

See also

sorted_list(), minimum_value(), maximum_value(), median_value(), quartile_value()

Notes

  • Set of numbers: \(a_i = \{ a_1, a_2, \cdots, a_n \}\)

  • Minimum: \(a_{min} \leq a_j, \forall a_j \in a_i\)

  • Maximum: \(a_{max} \geq a_j, \forall a_j \in a_i\)

  • For sets with an odd amount of numbers:

    • First quartile: \(Q_1 = a_{\lceil n/4 \rceil}\)

    • Median: \(M = a_{\lceil n/2 \rceil}\)

    • Third quartile: \(Q_3 = a_{\lceil 3n/4 \rceil}\)

  • For sets with an even amount of numbers:

    • If \(n \text{ mod } 4 \neq 0\):

      • First quartile: \(Q_1 = a_{\lceil n/4 \rceil}\)

      • Median: \(M = \frac{a_{n/2} + a_{n/2 + 1}}{2}\)

      • Third quartile: \(Q_3 = a_{\lceil 3n/4 \rceil}\)

    • If \(n \text{ mod } 4 = 0\):

      • First quartile: \(Q_1 = \frac{a_{n/4} + a_{n/4 + 1}}{2}\)

      • Median: \(M = \frac{a_{n/2} + a_{n/2 + 1}}{2}\)

      • Third quartile: \(Q_3 = \frac{a_{3n/4} + a_{3n/4 + 1}}{2}\)

  • Five-Number Summary

Examples

Import five_number_summary function from regressions library
>>> from regressions.statistics.summary import five_number_summary
Determine the five number summary of the set [21, 53, 3, 68, 43, 9, 72, 19, 20, 1]
>>> summary_even = five_number_summary([21, 53, 3, 68, 43, 9, 72, 19, 20, 1])
>>> print(summary_even['q1'])
9.0
>>> print(summary_even['maximum'])
72.0
Determine the five number summary of the set [12, 81, 13, 8, 42, 72, 91, 20, 20]
>>> summary_odd = five_number_summary([12, 81, 13, 8, 42, 72, 91, 20, 20])
>>> print(summary_odd['q3'])
76.5
>>> print(summary_odd['minimum'])
8.0