Five number summary for ungrouped 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 ($\max$).


$\min$ : smallest observation of a data set,

$Q_1$ :first quartile of a data set,

$\text{median} = Q_2$ : median of a data set,

$Q_3$ : third quartile of a data set,

$\max$ : largest observation of a data set.

The formula for $i^{th}$ quartile is

$Q_i =$ Value of $\bigg(\dfrac{i(N+1)}{4}\bigg)^{th}$ observation, $i=1,2,3$


  • $N$ is the total number of observations.

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