## Summary statistic for grouped data

Summary statistic summarize and provide information about the sample data. It includes the minimum value of the data, first quartile ($Q_1$), median (i.e., $Q_2$), mean ($\overline{x}$), third quartile ($Q_3$) and the minimum value of the data.

Summary statistic includes

• minimum value ($\min$),
• first quartile ($Q_1$),
• $\text{median }$ ($Q_2$),
• sample mean ($\overline{x}$),
• third quartile ($Q_3$),
• maximum value ($\max$).

## Formula

### $\min$, $Q_1$, $\text{median}$, $\overline{x}$, $Q_3$ and $\max$

The mean of $X$ is denoted by $\overline{x}$ and is given by

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

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