find the mode of the frequency distribution table given below class interval 0-10, 10-20, 20-30, 30-40, 40-50 frequency 7, 9, 15,

1 thought on “find the mode of the frequency distribution table given below class interval 0-10, 10-20, 20-30, 30-40, 40-50 frequency 7, 9, 15,”

1. Given data is

   [tex]\begin{gathered} \begin{array}{|c|c|} \bf{x_i} & \bf{f_i} \\ 0 – 10 & 7 \\10 – 20 & 9 \\20 – 30 & 15 \\30 – 40 & 11 \\40 – 50 & 8 \end{array}\end{gathered}[/tex]

   We know,

   Mode is given by

   [tex]\boxed{ \boxed{\sf{Mode = l + \bigg(\dfrac{f_1 – f_0}{2f_1 – f_0 – f_2} \bigg) \times h }}}[/tex]

   Where,

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: l \: is \: lower \: limit \: of \: modal \: class[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: \sf{f_0} \: is \: frequency \: of \: class \: preceding \: modal \: class[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: \sf{f_1} \: is \: frequency \: of \: modal \: class[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: \sf{f_2} \: is \: frequency \: of \: class \: succeeding \: modal \: class[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: h \: is \: height \: of \: modal \: class[/tex]

   Now,

   Here,

   Modal class = 20 – 30

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: l = 20[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: h = 10[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: f_0 = 9[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: f_1 = 15[/tex]

   [tex] \: \: \: \: \: \: \: \: \bull \: \: \: \: \: \sf \: f_2 = 11[/tex]

   On substituting all these values in above formula,

   [tex]\rm :\longmapsto\:{{\bf{Mode = l + \bigg(\dfrac{f_1 – f_0}{2f_1 – f_0 – f_2} \bigg) \times h }}}[/tex]

   [tex]\rm :\longmapsto\:{{\bf{Mode = 20+ \bigg(\dfrac{15 – 9}{2 \times 15 – 9 – 11} \bigg) \times 10 }}}[/tex]

   [tex]\rm :\longmapsto\:{{\bf{Mode = 20+ \bigg(\dfrac{6}{30 -20} \bigg) \times 10 }}}[/tex]

   [tex]\rm :\longmapsto\:{{\bf{Mode = 20+ \bigg(\dfrac{6}{10} \bigg) \times 10 }}}[/tex]

   [tex]\rm :\longmapsto\:{{\bf{Mode = 20+ 6 }}}[/tex]

   [tex]\rm :\longmapsto\:{{\bf{Mode = 26 }}}[/tex]

   Additional Information :-

   1. Mean using Direct Method :-

   [tex]\dashrightarrow\sf Mean = \dfrac{ \sum f_i x_i}{ \sum f_i}[/tex]

   2. Mean using Short Cut Method :-

   [tex]\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i d_i}{ \sum f_i}[/tex]

   3. Mean using Step Deviation Method

   [tex]\dashrightarrow\sf Mean =A + \dfrac{ \sum f_i u_i}{ \sum f_i} \times h[/tex]

   4. Median :-

   [tex]\dashrightarrow\sf Median= l + \Bigg \{h \times \dfrac{ \bigg( \dfrac{N}{2} – cf \bigg)}{f} \Bigg \}[/tex]

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