Question

`1) Find the mode of the following distribution of marks obtainedvby 60 students
marks obtained 0-10 10-20 20-30 30-40 40-50 no of students 6 5 12 22 15
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Answer 1

Step-by-step explanation:

I hope it will be help full for you thanks

Answer 2

Solution :-

$\begin{array}{| c | c |}\cline{1-2} \bf Marks\:\:Obtained & \bf No.\:of\:Students \\ \cline{1-2} 0-10 &\sf 6 \\ \cline{1-2} 10-20 &\sf 5\\ \cline{1-2} 20-30 &\sf 12\\ \cline{1-2} 30-40 &\sf 22\\ \cline{1-2} 40-50 &\sf 15\\ \cline{1-2}\end{array}$

Here, maximum frequency is 22 and its corresponding class is 30 - 40 which is modal class.

$\star$ Lower Limit L = 30

$\star$ Class width H = 40 - 30 = 10

$\star$ Frequency of preceding class, $\sf f_0$ = 12

$\star$ Frequency of modal class , $\sf f_1$ = 22

$\star$ Frequency of succeeding class, $\sf f_2$ = 15

The formula of mode

$Mode = L + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times H$

= 30 + $\frac{22-12}{2\times 22-12-15}\times 10$

= 30 + $\frac{22-12}{44-12-15}\times 10$

= 30 + $\frac{10}{17} \times 10$

= 30 + $\frac{100}{17}$

= $\frac{17\times 30 + 100}{17}$

= $\frac{510 + 100}{17}$

= $\frac{610}{17}$

= 35.88

Answer :-

The mode of the given distribution of marks is 35.88