Question

A student noted the number of cars passing through a spot on a road for $100$ periods each of $3$ minutes and summarised it in the table given below. Find the mode of the data

Number of cars	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	$7$	$14$	$13$	$12$	$20$	$11$	$15$	$8$

Answer 1

From the given data, it can be observed that the maximum class frequency is $20$, belongings to $40-50$ class intervals.

We know,

$Mode=l+\frac{f-f_1}{2f-f_1-f_2}\times h$

$l=$ lower limit of the modal class

$h=$ size of the class intervals

$f=$ frequency of the modal class

$f_1=$ frequency of the class preceding the modal class

$f_2=$ frequency of the class succeed in the modal class.

$\Rightarrow$ Modal class $=40-50$.

$\Rightarrow$ $l=40,f=20,f_1=12,f_2=11,h=10$

$\Rightarrow$ $Mode=40+\frac{20-12}{2\times 20-12-11}\times 10$

$\Rightarrow$ $Mode=40+\frac{80}{17}$

$\Rightarrow$ $Mode=40+4.71=44.7cars$