Find the mean marks from the following data:
Marks
Number of students
Below 10
5
Below 20
9
Below 30
17
Below 40
29
Below 50
45
Below 60
60
Below 70
70
Below 80
78
Below 90
83
Below 100
85

37.12

marks

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41.5

marks

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44.26

marks

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48.4

marks

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Solution

The correct option is D $48.4$ marks
Answer:- Taking continuous class interval with width $= 10$
$∴$ For $" 90 - 100 "= B e l o w 100 - B e l o w 90 = 85 - 83 = 2$
$∴$ For $" 80 - 90 "= B e l o w 90 - B e l o w 80 = 83 - 78 = 5$
Similarly for other classes also.
Thus our frequency distribution table is

Marks Students
$f_{i}$ $x_{i} = \frac{lower limit + upper limit}{2}$ $f_{i} x_{i}$
0-10 5 5 25
10-20 4 15 60
20-30 8 25 200
30-40 12 35 420
40-50 16 45 720
50-60 15 55 825
60-70 10 65 650
70-80 8 75 600
80-90 5 85 425
90-100 2 95 190
$Σ f_{i} = 85$ $Σ f_{i} x_{i} = 4115$
$∴$ Mean $= 48.4$

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Similar questions

Q. Find the mean marks from the following data(nearest integer)

Marks	No. of Students
Below 10	5
Below 20	9
Below 30	17
Below 40	29
Below 50	45
Below 60	60
Below 70	70
Below 80	78
Below 90	83
Below 100	85

Q. Find the mean marks from the following data:

Marks	No. of students
Below $10$	$4$
Below $20$	$10$
Below $30$	$18$
Below $40$	$28$
Below $50$	$40$
Below $60$	$70$

In a science test given to 10 students, the following marks [out of 100] are

recorded as: 77, 43, 39, 56, 96, 47, 53, 45, 45, 55.

Find out the mean & median of the above marks. [3 MARKS]

Using step - deviation method, calculate the mean marks of the following distribution.

$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 50 - 55 & 5 55 - 60 & 20 60 - 65 & 10 65 - 70 & 10 70 - 75 & 9 75 - 80 & 6 80 - 85 & 12 85 - 90 & 8 \end{matrix}$

The marks obtained by 12 students in a mathematics examination are given below.

48, 78, 93, 90, 66, 54, 83, 58, 60, 75, 89, 84.

Find (i) the mean of the marks; (ii) the mean mark of the students if each student is given 4 grace marks.

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Marks	Number of students
Below 10	5
Below 20	9
Below 30	17
Below 40	29
Below 50	45
Below 60	60
Below 70	70
Below 80	78
Below 90	83
Below 100	85

Marks	Students $f_{i}$	$x_{i} = \frac{lower limit + upper limit}{2}$	$f_{i} x_{i}$
0-10	5	5	25
10-20	4	15	60
20-30	8	25	200
30-40	12	35	420
40-50	16	45	720
50-60	15	55	825
60-70	10	65	650
70-80	8	75	600
80-90	5	85	425
90-100	2	95	190
	$Σ f_{i} = 85$		$Σ f_{i} x_{i} = 4115$

Find the mean marks from the following data:MarksNumber of studentsBelow 105Below 209Below 3017Below 4029Below 5045Below 6060Below 7070Below 8078Below 9083Below 10085

Find the mean marks from the following data:
Marks
Number of students
Below 10
5
Below 20
9
Below 30
17
Below 40
29
Below 50
45
Below 60
60
Below 70
70
Below 80
78
Below 90
83
Below 100
85