If the mean of the following distribution is $24$ , find the value of 'a'.
Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
Number of students $7$ a $8$ $10$ $5$

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Solution

Each of the intervals can be replaced by its mean for this calculation.
Mean of distribution = $24$ ,
Number of students = $30 + a$ ,
So, total marks awarded to all students = $24 \times (30 + a)$
total marks awarded to all students = $5 \times 7 + 15 \times a + 25 \times 8 + 35 \times 10 + 45 \times 5 = 810 + 15 a$
So, we have $24 (30 + a) = 810 + 15 a \Rightarrow a = 10$
So, the value of $a$ is $10$ .

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Marks	0-10	10-20	20-30	30-40	40-50
Number of students	15	20	35	p	10

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Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
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Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
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