C.I. 0-4 4-8 8-12 12-16 16-20
f 5 6 19 12 8
Find the mode of the following data:

10.6

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12

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12.6

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8

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Solution

The correct option is A $10.6$
CI Frequency(f)
0-4 5
4-8 6
8-12 19
12-16 12
16-20 8

Since the class $8 - 12$ has the highest frequency, therefore, it is the modal class
Now, Mode $= l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$
Where $l$ lower limit of the modal class
$f_{1} =$ frequency of the modal class
$f_{0} =$ frequency of the class preceeding the modal class
$f_{2} =$ frequency of the class succeeding the modal class
$h =$ size of the class interval
So, Mode $= 8 + \frac{19 - 6}{2 (19) - 6 - 12} \times 4 = 10.6$ .

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Similar questions

$x$	$5$	$10$	$12$	$15$	$20$	$30$	$40$
$f$	$4$	$8$	$11$	$13$	$16$	$12$	$9$

:

$X$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$	$12 - 14$	$14 - 16$
$F$	$1$	$2$	$2$	$3$	$6$	$3$	$2$

x	5	6	10	12	13	15
f	7	8	15	13	9	8

Class interval	0-4	4-8	8-12	12-16
Frequency	4	8	5	6

Class	$4 - 8$	$8 - 12$	$12 - 16$	$16 - 20$	$20 - 24$	$24 - 28$
Frequency	$9$	$6$	$12$	$7$	$15$	$3$

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