Five number summary for grouped data

A five number summary is a quick and easy way to determine the the center, the spread and outliers (if any) of a data set.

Five number summary includes five values, namely,

  • minimum value ($\min$),
  • first quartile ($Q_1$),
  • $\text{median }$ ($Q_2$),
  • third quartile ($Q_3$),
  • maximum value ($\max$).


$\min$= lower limit of the first class,

$\max$= upper limit of the last class,

$Q_i=l + \bigg(\dfrac{\dfrac{iN}{4} - F_<}{f}\bigg)\times h$ ; $i=1,2,\cdots,3$


  • $l$ is the lower limit of the $i^{th}$ quartile class
  • $N=\sum f$ total number of observations
  • $f$ frequency of the $i^{th}$ quartile class
  • $F_<$ cumulative frequency of the class previous to $i^{th}$ quartile class
  • $h$ is the class width

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