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

Answer:

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.

$\bigstar \: \: \large\underline{\underline{ \rm Answer : - }}$

$\longrightarrow$ 38.33

$\bigstar \: \: \large\underline{\underline{ \rm Given : - }}$

class interval :- 25-30,30-35,35-40,40-45,45-50,50-55.

ftequency:25,34,50,42,38,15.

$\bigstar \: \: \large\underline{\underline{ \rm Solution : - }}$

$\sf{\boxed{ \sf \: class \: interval \: \mid 25 - 30\mid \: 30 - 35\mid \: 35 - 40 \mid \: \: 40 - 45 \mid \: 45 - 50\mid \: 50 - 55 \mid } }$

$\sf{\boxed{ \sf \: frequency \: \: \: \: \: \: \mid 25 \: \: \: \: \: \: \: \: \: \: \mid \: 34 \: \: \: \: \: \: \: \: \: \mid \: 50 \: \: \: \: \: \: \: \: \: \mid \: \: 42 \: \: \: \: \: \: \: \: \: \: \: \mid \: 38 \: \: \: \: \: \: \: \: \: \: \: \: \mid \: 14 \: \: \: \: \: \: \: \: \: \: \: \: \mid } }$

Here is maximum frequency is 50 then the corresponding class 35 - 40 is the model class

L = 35 , h = 40 - 35 = 5 ,f = 50 ,$\rm{f_1}$ = 34 ,$\rm{f_2}$ = 42.

$\: \: \: \: \rm \: \: mode \: = L + \frac{f - f_1}{2f -f_1 - f_2} \times h$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: = 35 + \frac{50 - 34}{2 \times 50 - 34 - 42} \times 5$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: = 35 + \frac{16 \times 5}{24}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\rm \: = 35 + \frac{80}{24}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{ \rm \: = 38.33}$

$\huge{\bf{\pink{\fcolorbox{yellow}{black}{\underline{\color{aqua}{Høpe thîs helps u}}}}}} \:$