## 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 ($\max$).

## Formula

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

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

`$Q_i=l + \bigg(\dfrac{\dfrac{iN}{4} - F_<}{f}\bigg)\times h$`

; `$i=1,2,\cdots,3$`

where

- $l$ 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