From the following table the Arithmatic mean of marks obtained by students is $25$ , then find the value of $A$ .
Marks 0-10 10-20 20-30 30-40 40-50
Students $3$ $A$ $6$ $10$ $5$

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Solution

Mean $= \frac{S u m o f a l l v a l u e s}{T o t a l n u m b e r o f v a l u e s}$
The arithmetic mean of given data = $\frac{(5 \times 3) + (15 \times A) + (25 \times 6) + (35 \times 10) + (45 \times 5)}{3 + A + 6 + 10 + 5} = 25$
$\Rightarrow \frac{740 + 15 A}{24 + A} = 25$
$\Rightarrow 740 + 15 A = 24 \times 25 + 25 A$
$\Rightarrow 10 A = 740 - 600 = 140$
$\Rightarrow A = \frac{140}{10} = 14$
$∴$ the value of A is $14$ .

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