The mode for the frequency distribution
class interval 0-4 4-8 8-12 12-16
frequency 4 8 5 6

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5.28

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6.28

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Solution

The correct option is D 6.28
Here The maximum frequency is $f_{1} = 8$ whuch occur in Modal class 4-8.

Lower limit of Modal class= $L = 4$
class interval of Modal class= $h = 4$
frequency of Modal class= $f_{1} = 8$
Frequency of class preceeding the Modal class= $f_{0} = 4$
Frequency of class succeeding the Modal class= $f_{2} = 5$

$∴$
Mode $M = L + [\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}] \times h$

$⟹ M = 4 + [\frac{8 - 4}{2 \times 8 - 4 - 5}] \times 4 ⟹ M = 4 + \frac{4}{7} \times 4 = 4 + 2.28 = 6.28$

Hence Mode $M = 6.28$

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Similar questions

Size of items:	0-4	4-8	8-12	12-16	16-20	20-24	24-28	28-32	32-36	36-40
Frequency:	5	7	9	17	12	10	6	3	1	0

C.I	0-4	4-8	8-12	12-16	16-20	20-24
frequency	4	7	10	15	11	6

14.4

20.

Class interval	0-6	6-12	12-18	18-24	24-30
Frequency	4	x	5	y	1

Class-interval	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	10	35	52	61	38	20

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Class	$33$	$44$	$55$	$66$	$77$	$88$	$99$
Frequency	$12$	$3$	$90$	$100$	$100$	$10$	$6$

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