Question

Find the sum of lower limit of modal class and median of the following data: 30-40......25, 40-50......30, 50-60...16, 60-70...19, 70-80....17, 80-90.....18 ?

Answer 1

$\begin {array}{|c|c|} \cline{1-2} Data &frequency \\ \cline{1-2} 30-40 &25 \\ \cline{1-2}40-50&30 \\\cline{1-2}50-60&16 \\\cline{1-2}60-70&19 \\\cline{1-2}70-80&17 \\\cline{1-2}80-90&18 \\ \cline{1-2}Total \: frequency&125\\ \cline{1-2}\end{array}$

$\mathsf{Since, \: frequency \: is \: odd \: median \: will \: be}$

$\huge \boxed{median = \dfrac{{n +1}^{th}}{2} term}$

$\mathsf{median = \dfrac{{125 +1}^{th}}{2} term}$

$\mathsf{median = \dfrac{{126}^{th}}{2} term}$

$\mathsf{median = 68 term}$

$\mathsf{median= 19}$

◼
$\mathsf{For \: lower \: quatile,}$

$\huge \boxed{lower \: quatile = \dfrac{1}{4}\times {n +1}^{th}term}$

$\mathsf{lower \: quatile = \dfrac{1}{4}\times {126}^{th}term}$

$\mathsf{lower \: quatile = 31.5term}$

$\mathsf{lower \: quatile = 25}$