The frequency distribution of marks obtained by $28$ students in a test carrying $40$ marks is given below
Marks 0-10 10-20 20-30 30-40
Number of students 6 $x$ $y$ 6

If the mean of the above data is $20$ , then the difference between $x$ and $y$ is

3

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2

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1

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0

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Solution

The correct option is C $0$
Total number of student is 28. $\Rightarrow x + y + 6 + 6 = 28 \Rightarrow x + y = 16$ (i)
And mean $= \frac{5 \times 6 + 15 x + 25 y + 35 \times 6}{28} = 20$ (given)
$\Rightarrow 3 x + 5 y = 64$ (ii)
Solving these two equation we get, $x = 8, y = 8$

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Similar questions

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	$x$	15	16	6

x

Marks	:	0-10	10-20	20-30	30-40	40-50
No. of Students	:	3	10	14	10	3

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of Students	12	18	27	20	17	6

100

50

Marks	0-9	10-19	20-29	30-39	40-49
No. of students	8	15	20	45	12

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

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