Quartiles for grouped data

Quartiles are the values of arranged data which divide whole data into four equal parts. They are 3 in numbers namely $Q_1$, $Q_2$ and $Q_3$. Here $Q_1$ is first quartile, $Q_2$ is second quartile and $Q_3$ is third quartile.

Formula

For discrete frequency distribution, the formula for $i^{th}$ quartile is

$Q_i =\bigg(\dfrac{i(N)}{4}\bigg)^{th}$ value, $i=1,2,3$

where,

  • $N$ is total number of observations.

For continuous frequency distribution, the formula for $i^{th}$ quartile is

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

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

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