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
$7$
$14$
$13$
$12$
$20$
$11$
$15$
$8$

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Solution

Mode: The class which have highest frequency.
In this case, class interval $40 - 50$ is the modal class.

Now,
Lower limit of modal class, $l = 40, h = 10, f_{1}, = 20, f_{0} = 12, f_{2} = 11$

We know that,
Mode $= l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 40 + (\frac{20 - 12}{2 (20) - 12 - 11}) \times 10$

$= 40 + (\frac{8}{40 - 23}) 10$

$= 40 + (\frac{8}{17}) \times 10$

Mode $\equiv 44.7$
Hence, the mode of the given data is $44.7$ cars.

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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

Q. 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	$7$	$9$	$13$	$21$	$12$	$15$	$4$	$12$

Question 6
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data.

$\begin{matrix} Number of cars & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 Frequency & 7 & 14 & 13 & 12 & 20 & 11 & 15 & 8 \end{matrix}$