The approximate mean for the following distribution is 7

$\begin{matrix} x : & 5 & 6 & 7 & 8 & 9 f : & 4 & 8 & 14 & 11 & 3 \end{matrix}$

True

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False

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Solution

$\begin{matrix} x_{i} & f_{i} & x_{i} \times f_{i} 5 & 4 & 20 6 & 8 & 48 7 & 14 & 98 8 & 11 & 88 9 & 3 & 27 T o t a l & 40 & 281 \end{matrix} ∴ M e a n (¯ x) = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{281}{40} = 7.025$

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\begin{matrix} x f \end{matrix} \begin{matrix} 57 \end{matrix} \begin{matrix} 106 \end{matrix} \begin{matrix} 158 \end{matrix} \begin{matrix} 20 K \end{matrix} \begin{matrix} 255 \end{matrix}

Find the missing value of $p$ for the following distribution whose mean is 12.58.

$\begin{matrix} x : & 5 & 8 & 10 & 12 & p & 20 & 25 f : & 2 & 5 & 8 & 22 & 7 & 4 & 2 \end{matrix}$

x:	5	6	7	8	9
f:	4	8	14	11	3

$x$ :	$5$	$6$	$7$	$8$	$9$
$f$ :	$4$	$8$	$14$	$11$	$3$

\begin{matrix} 14 & 11 & (75) 11 & 7 & (54) 9 & 8 & (. . . .) \end{matrix}

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