Question

Weight (in kg) :- 40-45, 45-50, 50-55, 55-60,60-65, 70-75

No.of students:- 2,3,8,6,6,3,2

Find the median weight.​

Answer 1

★ Solution :

$\begin{tabular}{|c|c|c|c|c|c|c|c|}\cline{1-8} \tt Weight (In kg) & \tt 40-45 & \tt 45-50 & \tt 50-55 & \tt 55-60 & \tt 60-65 & \tt 65-70 & \tt 70-75 \\\cline{1-8}\tt No. of Students &\tt 2& \tt 3& \tt 8 & \tt 6 & \tt 6 & \tt 3 & \tt2\\\cline{1-8}\end{tabular}$

$\boxed{\begin{array}{cccc}\sf Weight\: (In\:kg)&\sf No. of\: Students&\sf Cumulative\:Frequency\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 40-45&\sf 2&\sf 2 \\\\\sf 45-50 &\sf 3&\sf 2+3=5 \\\\\sf 50-55 &\sf 8 &\sf 7+8=13 \\\\\bf 55-60&\bf 6 &\bf 13 + 6 = 19\\\\\sf 60-65 &\sf 6 &\sf 19+6=25 \\\\\sf 65-70 &\sf 3 &\sf 25+3=28\\\\\sf 70-75 &\sf 2 &\sf 28+2=30\end{array}}$

$\rule{130}{1}$

$:\implies\sf N=\sum\limits f\\\\\\:\implies\sf \dfrac{N}{2} = \dfrac{\sum\limits f}{2}\\\\\\:\implies\sf \dfrac{N}{2} = \dfrac{30}{2}\\\\\\:\implies\sf\dfrac{N}{2} = 15 \\\\\underline{\textsf{Hence, 50 - 60 is the median class.}}$

$\boxed{\begin{minipage}{6cm} \bigstar \:\:\sf Median = l + \sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here:\\1)\:l=Lower\:limit\:of\:median\:class=55\\2)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=13\\3)\:f= frequency\:of\:median\:class=6\\4)\:h= Class\:interval =40-45=5\end{minipage}}$

$\rule{170}{2}$

☯$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\dashrightarrow\sf\:\:Median = l +\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\\\\dashrightarrow\sf\:\:Median = 55 +\bigg\lgroup\dfrac{15-13}{6}\times5\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:Median = 55 +\bigg\lgroup\dfrac{2}{6}\times 5\bigg\rgroup\\\\\\\dashrightarrow\sf\:\:Median = 55 + 1.67 \\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Median = 56.67}}$

⠀

$\therefore\:\underline{\textsf{Median Height of the distribution is \textbf{56.67 kg}}}.$

Answer 2

Step-by-step explanation:

Median height of the distribution is 56.67 kg.

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