## 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

### $\max$ : 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.