Question

answer kardo please I'll mark you as braiiest​

Answer 1

$\large\underline{\sf{Solution-}}$

$\begin{gathered} \begin{array}{|c|c|} \bf{class} & \bf{frequency} \\ 1 - 3 & 7  \\3 - 5 & 8 \\5 - 7 & 12 \\7 - 9 & 2 \\9 - 11 & 1 \end{array}\end{gathered}$

We know that ,

Formula for Mode is

$\boxed{ \boxed{\bf{Mode = l + \bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h }}}$

where,

$\: \: \: \: \: \: \: \: \: \bull \sf \: l \: is \: lower \: limit \: of \: modal \: class$

$\: \: \: \: \: \: \: \: \: \bull \sf \: \sf{f_0} \:  is \: frequency \: of \: class \: preceding \: modal \: class$

$\: \: \: \: \: \: \: \: \: \bull \sf \: \sf{f_1} \: is \: frequency \: of \: modal \: class$

$\: \: \: \: \: \: \: \: \: \bull \sf \: \sf{f_2} \: is \: frequency \: of \: class \: succeeding \: modal \: class$

$\: \: \: \: \: \: \: \: \: \bull \sf \: h \: is \: height \: of \: modal \: class$

Here,

Modal class is 5 - 7

So,

$\: \: \: \: \: \: \: \: \: \bull \sf \: l \: = \: 5$

$\: \: \: \: \: \: \: \: \: \bull \sf \: f_0 \: = \: 8$

$\: \: \: \: \: \: \: \: \: \bull \sf \: f_1 \: = \: 12$

$\: \: \: \: \: \: \: \: \: \bull \sf \: f_2 \: = \: 2$

$\: \: \: \: \: \: \: \: \: \bull \sf \: h \: = \: 2$

Thus,

$\rm :\longmapsto\:{{\bf{Mode = l + \bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h }}}$

$\rm :\longmapsto\:{{\bf{Mode = 5 + \bigg(\dfrac{12 - 8}{2 \times 12 - 8 - 2} \bigg) \times 2}}}$

$\rm :\longmapsto\:{{\bf{Mode = 5 + \bigg(\dfrac{4}{24 - 10} \bigg) \times 2}}}$

$\rm :\longmapsto\:{{\bf{Mode = 5 + \bigg(\dfrac{4}{14} \bigg) \times 2}}}$

$\rm :\longmapsto\:{{\bf{Mode = 5 + \bigg(\dfrac{4}{7} \bigg)}}}$

$\rm :\longmapsto\:{{\bf{Mode = 5 + 0.57}}}$

$\rm :\longmapsto\:{{\bf{Mode = 5.57}}}$

Additional Information :-

$\boxed{ \sf Median= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} - cf \bigg)}{f} \Bigg \}}$

$\dashrightarrow\sf Mean = \dfrac{ \sum f_i x_i}{ \sum f_i}$

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i}$

$\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h$