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

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

Filo · Accepted Answer

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.

Question Text	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:
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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