If the mean of the following distribution is 6, then value of p is
$x : 24610 p + 5$
$f : 32312$

5

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7

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6

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12

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Solution

The correct option is B $7$
$6 = \frac{(2 \times 3) + (4 \times 2) + (6 \times 3) + (10 \times 1) + (p + 5) \times 2}{3 + 2 + 3 + 1 + 2}$

$\Rightarrow 6 = \frac{6 + 8 + 18 + 10 + 2 p + 10}{11}$
$\Rightarrow 6 = \frac{52 + 2 p}{11}$
$\Rightarrow 6 \times 11 = 52 + 2 p$
$\Rightarrow 66 - 52 = 2 p$
$\Rightarrow 14 = 2 p$
$\Rightarrow p = \frac{14}{2}$
$∴ p = 7$

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If $\sum f x = 5 x + 2$ and $\sum f = 12$ and the mean of the distribution is 6, then the value of $x$ is less than _____.

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