Five Number Summary and Boxplot

 Shape of a distribution can be obtained with five numbers value:

  • Minimum
  • Quartile1(Q1)
  • Median (Q2)
  • Quartile3 (Q3)
  • Maximum

IQR can be found from Q1and Q3, hence outliers. Median will provide the central tendency of data. Minimum and Maximum value gives end points of data. Hence, complete distribution of data can be interpreted from Five number summary.

Boxplot

  • Boxplots are popular way of visualising a distribution. It incorporate the five number summary.
  • Ends of the box are at quartiles so that the box length is the interquartile range.
  • The median is marked by a line within the box.


Whiskers: Two lines outside if the box, extended to the smallest (Min) and largest (Max) observation are called Whiskers.

  • The whiskers are extended to the extreme low and high observations only if these values are less than 1.5 x IQR beyond the outliers.
  • The remaining cases are plotted individually.

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