## 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

### $Q_i=l + \bigg(\dfrac{\dfrac{iN}{4} - F_<}{f}\bigg)\times h$ ; $i=1,2,\cdots,3$

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