Summary statistic for ungrouped 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
$\overline{x} =\dfrac{1}{n}\sum_{i=1}^{n}x_i$
Quartiles
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.
