Question

Find the median of the following data​

Answer 1

$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \tt Class & \tt 0-20 & \tt 20-40 & \tt 40-60 & \tt 60-80 & \tt 80-100 \\\cline{1-6}\tt Frequency &\tt 5 & \tt 15& \tt 30 & \tt 8 & \tt 2 \\\cline{1-6}\end{tabular}\end{gathered}$

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We have to find, Median of given data.

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$\boxed{\begin{array}{cccc}\sf Class\: mark \: (x)&\sf Frequency \: (f)&\sf CF\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 5 - 20&\sf 5&\sf 5\\\\\sf 20 - 40&\sf 15&\sf 20\\\\\sf 40 - 60&\sf 30&\sf 50 \\\\\sf 60 - 80&\sf 8&\sf 58\\\\\sf 80 - 100&\sf2&\sf 60\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf&\sf \sum f = 60&\sf\end{array}}$

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$\dag\;{\underline{\frak{We\;know\;that,}}}$

$\boxed{\begin{minipage}{6cm} \bigstar \:\:\sf Median = l + \sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here:\\1)\:l=Lower\:limit\:of\:median\:class=40\\2)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=20\\3)\:f= frequency\:of\:median\:class=30\\4)\:h= Class\:interval =60-40=20\end{minipage}}$

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$\dag\;{\underline{\frak{Formula\;to\:find\;Median,}}}$

$\star\;{\boxed{\sf{\pink{l + \dfrac{ \frac{n}{2} - C.F.}{f} \times h}}}}$

${\underline{\sf{\bigstar\;Putting\;values\;in\;formula\;:}}}$

$:\implies\sf 40 + \dfrac{ \frac{60}{2} - 20}{30} \times 20$

$:\implies\sf 40 + \dfrac{30 - 20}{30} \times 20$

$:\implies\sf 40 + \dfrac{10}{30} \times 20$

$:\implies\sf 40 + \dfrac{20}{3}$

$:\implies\sf 40 + 6.66$

$:\implies{\underline{\boxed{\sf{\purple{46.66}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Median\;of\;given\; distribution\;is\;{\textsf{\textbf{46.66}}}.}}}$