Question

A student noted that the number of cars passing through the spot on the road for $200$ periods each of $10$ minutes and summarized in a 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	$7$	$9$	$13$	$21$	$12$	$15$	$4$	$12$

• A. $34.71$
• B. $36.47$
• C. $42.63$
• D. $47.26$

Answer 1

Answer: (A)

$34.71$

The maximum frequency is $21,$ the class corresponding to that frequency is equal to $30-40$

We have to apply the formula Mode$=L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

Where L is the lower class limit of the modal class $=30$

$f_1$is the

frequency of the modal class $=21$

$f_0$is the frequency of the class before the modal class in the frequency table $=13$

$f_2$ is the frequency of the class after the modal class in the frequency table $=12$

h is the class interval of the modal class $=10$

Mode$=30\left[\right(21-13\left)/\right([2\times 21]-18-12\left)\right]\times 10$

$=30+\left[\right(8)/42-18-12]\times 10$

$=3+\left[8/12\right]\times 10$

$=3+6.67$

Hence, mode$=9.67$