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 ($\max$).


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

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

$\overline{x} =\dfrac{1}{n}\sum_{i=1}^{n}x_i$

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


  • $l$ 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

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