Question

find the mode of given data

class:- 1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500 4500-5000
frequency:- 14 56 60 86 74 62 48


step by step plss​

Answer 1

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

Given data is

$\begin{gathered} \begin{array}{|c|c|} \bf{x_i} & \bf{f_i} \\ 1500 - 2000 & 14  \\2000 - 2500 & 56 \\2500 - 3000 & 60 \\3000 - 3500 & 86 \\3500 - 4000 & 74\\4000 - 4500 & 62\\4500 - 5000 & 48 \end{array}\end{gathered}$

We know,

Mode is evaluated as

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

where,

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

$\: \: \: \: \: \: \: \: \bull \rm \: f_0 \: is \: frequency \: of \: class \: preceeding \: modal \: class$

$\: \: \: \: \: \: \: \: \bull \rm \: f_1 \: is \: frequency \: of \: modal \: class$

$\: \: \: \: \: \: \: \: \bull \rm \: f_2 \: is \: frequency \: of \: class \: succeeding \: modal \: class$

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

Here,

Modal class = 3000 - 3500

$\: \: \: \: \: \: \: \: \bull \rm \: l = 3000$

$\: \: \: \: \: \: \: \: \bull \rm \: h = 500$

$\: \: \: \: \: \: \: \: \bull \rm \: f_0 = 60$

$\: \: \: \: \: \: \: \: \bull \rm \: f_1 = 86$

$\: \: \: \: \: \: \: \: \bull \rm \: f_2 = 74$

On substituting all these values in formula of mode, we have

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

$\rm :\longmapsto\:{{\sf{Mode = 3000 + \bigg(\dfrac{86 - 60}{2 \times 86 - 60 - 74} \bigg) \times 500 }}}$

$\rm :\longmapsto\:{{\sf{Mode = 3000 + \bigg(\dfrac{26}{172 - 134} \bigg) \times 500 }}}$

$\rm :\longmapsto\:{{\sf{Mode = 3000 + \bigg(\dfrac{26}{38} \bigg) \times 500 }}}$

$\rm :\longmapsto\:{{\sf{Mode = 3000 + 342.105 }}}$

$\rm :\longmapsto\:{{\sf{Mode = 3342.105 }}}$

Additional Information :-

Mean using Direct Method :-

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

Mean using Short Cut Method

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

Mean using Step Deviation Method

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

Median

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

Answer 2

Step-by-step explanation:

solve in deviation method with calcilation