Question

please please answer this​

Answer 1

Answer:

$\begin{tabular}{|c |c | c|}\cline{1-3}\bf \underline {Weight (in kg)}&\bf\underline {No. of students(f)}&\bf\underline {c.f}\\\cline{1-3}\sf 40-45 & \sf 2 & \sf 2 \\\sf 45-50 & \sf 3 & \sf 5 \\\sf 50-55 &\sf 8 & \sf 13\\\sf 55-60 &\sf 6 &\sf 19\\\sf 60-65 & \sf 6 &\sf 25 \\\sf 65-70 &\sf 3 &\sf 28 \\\sf 70-75 &\sf 2 &\sf 30 \\\cline{1-3}\end{tabular}$

n = $\sf \sum fi$

n/2 = 30/2 = 15

Therefore, 55 - 60 is the median class.

• lower limit (l) = 55

• class interval (h) = 45 - 40 = 5

• CF = 13

• frequency (f) = 6

➨ Median = $\sf \ l\ +\ \dfrac{\frac{n}{2}\ -\ cf}{f}\ \times\ h$

➨ Median = $\sf 55 + \dfrac{15-13}{6} \times 5$

➨ Median = $\sf 55 + \dfrac{2}{6} \times 5$

➨ Median = $\sf 55 + 1.67$

➨ Median = $\pink{\sf 56.67}$

So, median weight is 56.67 kg.

Answer 2

★ Solution :

$\boxed{\begin{array}{cccc}\sf Weight \:(in\:kg)&\sf Number \:of\: students &\sf Cumulative\: frequency \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 40-45&\sf 2&\sf 2 \\\\\sf 45-50 &\sf 3&\sf 2 + 3 = 5 \\\\\sf 50-55 &\sf 8&\sf 5 + 8 = 13\\\\\bf 55-60 &\bf 6&\bf 13 + 6 = 19 \\\\\sf 60-65 &\sf 6&\sf 19 + 6 = 25\\\\\sf 65-70 &\sf 3&\sf 25 + 3 = 28\\\\\sf 70-75 &\sf 2&\sf 28 + 2 = 30\end{array}}$

$\rule{130}{1}$

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

$\boxed{\begin{minipage}{6cm} \bigstar \:\:\sf Median = l + \sf\dfrac{\frac{n}{2}-C.f.}{f}\times h\\\\Here:\\1)\:l=Lower\:limit\:of\:median\:class=50\\2)\:C.f.=Cumulative\:frequency\:of\:class\\preceeding\:the\:median\:class=13\\3)\:f= frequency\:of\:median\:class=6\\4)\:h= Class\:interval =45-40=5\end{minipage}}$

$\rule{170}{2}$

$\underline{\bigstar\:\textbf{According to the Question :}}$

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

⠀

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