If the mean of the following frequency distribution is $5$ , then $b$ is equal to
$x_{i}$ : 3 5 7 4
$f_{i}$ : 2 $a$ 5 $b$

10

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6

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8

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None of these

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Solution

The correct option is D $6$
We have
$\frac{3 \times 2 + 5 \times a + 7 \times 5 + 4 \times b}{2 + a + 5 + b} = 5$
$\Rightarrow = 5 a + 4 b + 41 = 35 + 5 a + 5 b \Rightarrow b = 6$

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