Question

find the mode of following ferquency distribution. class interval: 25-30,30-35,35-40,40-45,45-50,50-55. ftequency:25,34,50,42,38,15​

Answer 1

$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Class & \tt 25-30 & \tt 30-35 & \tt 35-40 & \tt 40-45 & \tt 45-50 & \tt 50-55 \\\cline{1-7}\tt Frequency &\tt 25 & \tt 34 & \tt 50 & \tt 42 & \tt 38 & \tt 15 \\\cline{1-7}\end{tabular}\end{gathered}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

Here, Maximum frequency is 50.

Then, the corresponding class 35-40 is the model class.

⠀⠀⠀⠀

$\bf{\dag}\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Mode = L + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h}}}}$

Here,

⠀⠀⠀⠀

• L = Lower limit = 35
• h = Class height = 40 - 35 = 5
• $\sf f_0$, Frequency of the preceding class = 34
• $\sf f_1$, = Frequency of the Model class = 50
• $\sf f_2$, Frequency of the succeeding class = 42

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\bf{\dag}\;{\underline{\frak{Putting\:values\:in\:formula,}}}$

$:\implies\sf 35 + \dfrac{50 - 34}{(2 \times 50) - 34 - 42} \times 5$

$:\implies\sf 35 + \dfrac{16}{100 - 34 - 42} \times 5$

$:\implies\sf 35 + \dfrac{16}{24} \times 5$

$:\implies\sf 35 + \dfrac{80}{24}$

$:\implies\sf 35 + 3.33$

$:\implies{\underline{\boxed{\frak{\purple{38.33}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\:The\:mode\:of\:given\:data\;is\; {\textsf{\textbf{38.33}}}.}}}$

Answer 2

$\Large\bf\pink {GiVeN,}$

$\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Class & \tt 25-30 & \tt 30-35 & \tt 35-40 & \tt 40-45 & \tt 45-50 & \tt 50-55 \\ \cline{1-7}\tt Frequency &\tt 25 & \tt 34 & \tt 50 & \tt 42 & \tt 38 & \tt 15 \\ \cline{1-7}\end{tabular}$

$\Large\bf\orange{To\:FiNd,}$

• The mode of the given frequency distribution.

$\Large\bf\green{CaLcUlAtIoN,}$

☆ Here the maximum frequency is 50. And the corresponding class-interval is 35-40 (modal class ).

$\bf\red {We\:know\:that,}$

$\orange\bigstar\:\:\bf{\color{indigo}Mode\:=\:L\:+\:\Big (\dfrac{f_1\:-\:f}{2f_1\:-\:f\:-\:f_2}\Big)\:\times{h}\:}$

$\bf\red{Where,}$

• L = 35

• h = 40 - 35 = 5

• f = 34

• $\bf{f_1}$ = 50

• $\bf{f_2}$ = 42

$\longmapsto\:\:\bf{Mode\:=\:35\:+\:\Big\{\dfrac{50\:-\:34}{(2\times{50})\:-\:34\:-\:42}\Big\}\:\times{5}\:}$

$\longmapsto\:\:\bf{Mode\:=\:35\:+\:\Big(\dfrac{16}{100\:-\:34\:-\:42}\Big)\:\times{5}\:}$

$\longmapsto\:\:\bf{Mode\:=\:35\:+\:\dfrac{16}{24}\times{5}\:}$

$\longmapsto\:\:\bf{Mode\:=\:35\:+\:\dfrac{2}{3}\times{5}\:}$

$\longmapsto\:\:\bf{Mode\:=\:35\:+\:\dfrac{10}{3}\:}$

$\longmapsto\:\:\bf{Mode\:=\:35\:+\:3.33\:}$

$\longmapsto\:\:\bf\purple{Mode\:=\:38.33\:}$

$\Large\bf\therefore$ The mode of the given frequency distribution is 38.33.