## 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.