Below is given frequency distribution of marks (out of 100) obtained by the students.
Calculate mean marks scored by a student.
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

48.75

marks

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51.75

marks

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54.75

marks

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57.75

marks

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Solution

The correct option is A $51.75$ marks
$c i$ $f_{i}$ $x_{i}$ $f_{i} x_{i}$
0-10 3 5 15
10-20 5 15 75
20-30 7 25 175
30-40 10 35 350
40-50 12 45 540
50-60 15 55 825
60-70 12 65 780
70-80 6 75 450
80-90 2 85 170
90-100 8 95 760
Consider the following table, to calculate mean:
$N = Σ f_{i} = 80$
$Σ f_{i} x_{i} = 4140$

Mean $¯ ¯ ¯ x = \frac{Σ f_{i} x_{i}}{N}$
$∴ ¯ ¯ ¯ x = \frac{4140}{80} = 51.75$
Mean marks scored by a student is $51.75$
Hence, option $B$ is correct.

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Similar questions

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

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 obtained	0-20	20-40	40-60	60-80	80-100
No. of students	4	6	25	10	5

50

Marks	0-20	20-40	40-60	60-80	80-100
Numbers of students	6	11	17	12	4

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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
No. of Students	3	5	7	10	12	15	12	6	2	8