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 ($\max$).
Formula
$\min$ : 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, $i=1,2,3$
where,
- $N$ is the total number of observations.
