The marks in science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
Marks: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Frequency: 3 5 16 12 13 20 5 4 1 1

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Solution

Marks 0 – 10 10–20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

Frequency 3 5 16 12 13 20 5 4 1 1

Here the maximum frequency is 20, then the corresponding class 50 – 60 is the modal class

l = 50, h = 60 – 50 = 10, f = 20, f₁ = 13, f₂= 5
$Mode space equals space straight l plus fraction numerator straight f â�� straight f subscript 1 over denominator 2 straight f â�� straight f subscript 1 minus straight f subscript 2 end fraction cross times straight hspace space space space space space space space space space space space equals space 50 plus fraction numerator 20 â�� 13 over denominator 2 cross times 20 â�� 13 â�� 5 end fraction cross times 10space space space space space space space space space space space space equals space 50 space plus space 70 over 22space space space space space space space space space space space space equals space 50 space plus space 3.18space space space space space space space space space space space space equals space 53.18$

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80

C.I.	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Freq.	3	5	16	12	13	20	5	4	1	1

80

Marks:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency:	$3$	$5$	$16$	$12$	$13$	$20$	$5$	$4$	$1$	$1$

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
No. of Students	3	5	7	10	12	15	12	6	2	8

Marks obtained	0-10	10-20	20-30	30-40	40-50	50-60	60-70
No. of students	$2$	$10$	$12$	$15$	$13$	$8$	$4$

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Number of students	5	4	6	8	5	7	4	9	5	7

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Marks	0 – 10	10–20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	5	16	12	13	20	5	4	1	1