If $x < 6$ and $17.5$ is the mode of the following frequency distribution

Class
interval 0-5 5-10 10-15 15-20 20-25

Frequency 5 2 3 6 x

Then $x$ =

3

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2

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4

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5

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Solution

The correct option is A $3$
Clearly $15 - 20$ is the modal class such that
$l = 15, h = 5, f = 6, f_{1} = 3$ and $f_{2} = x$
$∴$ Mode $= l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h$
$\Rightarrow 17.5 = 15 + \frac{6 - 3}{12 - 3 - x} \times 5 \Rightarrow 2.5 x = 7.5 \Rightarrow x = 3$

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Similar questions

Class	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$
Frequency	$2$	$3$	$10$	$1$	$4$

15

a

Class Interval	$5$	$10$	$15$	$20$	$25$
Frequency	$6$	$a$	$6$	$10$	$5$

Class-interval	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
Frequency	$5$	$3$	$9$	$10$	$8$	$5$

Class:	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency:	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

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