The mean of following distribution is $6.5$ then find the value of $k .$

5

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4

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7

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8

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Solution

The correct option is C $7$
Answer:-

x f $x_{i} . f_{i}$
2 5 10
4 3 12
6 7 42
8 6 48
10 k 10k
$Σ f_{i} = 21 + k$ $Σ f_{i} . x_{i} = 112 + 10 k$
Mean = 6.5 (given)
Mean = $\frac{Σ f_{i} . x_{i}}{Σ f_{i}} = \frac{112 + 10 k}{21 + k} = 6.5$
$\Rightarrow \frac{112 + 10 k}{21 + k} = 6.5$
$\Rightarrow 3.5 k = 24.5$
$\Rightarrow k = \frac{24.5}{3.5} = 7$
C) 7

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If the mean of the following frequency distribution is $7.2$ find value of $k$ .

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$x$ :	$5$	$8$	$10$	$12$	$p$	$20$	$25$
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