Question

Find the mode of the following frequency distribution-
?
class interval 25-30 30-35 35 - 40 40-45 45-50 50-55
frequency
25 34 50 42 38 48​

Answer 1

$\begin{gathered}\begin{tabular}{|c|c|c|c|c|c|c|}\cline{1-7} \tt Class & \tt 25-30 & \tt 30-35 & \tt 35-40 & \tt 40-45 & \tt 45-50 & \tt 50-55\\\cline{1-7}\tt Frequency &\tt 25 & \tt 34 & \tt 50 & \tt 42 & \tt 38& \tt 48 \\\cline{1-7}\end{tabular}\end{gathered}$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\boxed{\begin{array}{cccc}\sf Class\: interval&\sf Frequency\: (f)\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 25-30&\sf 25\\\\\sf 30-35&\sf 34\\\\\sf 35-40 &\sf 50\\\\\sf 40-45&\sf 42\\\\\sf 45-50&\sf 38\\\\\sf 50-55&\sf 48\end{array}}$

⠀⠀⠀⠀

Here,

• Maximum frequency is 50 then the corresponding class 35-40 is the model class.

⠀⠀⠀⠀

Therefore,

• Lower limit, L = 35

• Class width, H = 40 - 35 = 5

• Frequency of preceding class, $\sf f_0$ = 34

• Frequency of modal class , $\sf f_1$ = 50

• Frequency of succeeding class, $\sf f_2$ = 42

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

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

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

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

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

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

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

$:\implies\sf 35 + 3.33$

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

$\therefore\;{\underline{\sf{Mode\:of\:the\:given\:data\:is\: {\textsf{\textbf{38.33}}}.}}}$