Question

Find the median of the following data Marks 20-30 30-40 40-50 50-60 60-70 70-80 80-90 frequency 5 15 25 20 7 8 10

Answer 1

$\sf \bold{\underline{Question:-}}$

Find the median of the following data :

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$\begin{tabular}{|c|c|c|c|c|c|c|c|}\cline{1-8} Class&20 - 30& 30 - 40 & 40 - 50&50 - 60&60 - 70&70 - 80&80 - 90\\\cline{1-8}Frequency&5&15&25&20&7&8&10\\\cline{1-8}\end{tabular}$

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$\sf \bold{\underline{AnswEr:-}}$

$\boxed{\begin{array}{cccc}\bf Class\: interval&\bf Frequency\: (f) &\bf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 20 - 30&\sf 5&\sf 5\\\\\sf 30 - 40 &\sf 15&\sf 20\\\\\sf 40 - 50&\sf 25&\sf 45\\\\\sf 50 - 60&\sf 20&\sf 65\\\\\sf 60 - 70&\sf 7&\sf 72\\\\\sf 70 - 80&\sf 8&\sf 80\\\\\sf 80 - 90&\sf 10&\sf 90\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf & \bf \sum f = 90& \end{array}}$

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We know that,

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$\boxed{\begin{minipage}{6cm} \bigstar \:\:\sf Median = l + \sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here: \\ \\1)\:N = \sum \:f= 90\\2)\:l=Lower\:limit\:of\:median\:class=40\\3)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=20\\4)\:f= frequency\:of\:median\:class=25\\5)\:h= Class\:interval =40-30=10\end{minipage}}$

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$\underline{\bigstar\:\boldsymbol{According\; to \;the \;Question :}}$

$\dashrightarrow\sf\:\:\purple{Median = l +\dfrac{\frac{n}{2}-C.f.}{f}\times h}\\\\\\\dashrightarrow\sf\:\:Median = 40 +\bigg\lgroup\dfrac{45-20}{25}\times10\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:Median = 40 +\bigg\lgroup \cancel{\dfrac{25}{25}}\times10\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:Median = 40 +10\\\\\\\dashrightarrow\:\:\underline{\boxed{\pink{\sf Median = 50}}}\;\bigstar$

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$\therefore\:\underline{\textsf{Median of given data is \textbf{50}}}.$

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