A set of data arranged in ascending order is given

3, 5, 10, 12, $x$ , 15, 20, 21, 29

Find the value of $x$ if mean of the given numbers is 12.

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Solution

Number of observations = 9

$M e a n = \frac{S u m o f t h e o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s} \Rightarrow 12 = \frac{3 + 5 + 10 + 12 + x + 15 + 20 + 21 + 29}{9}$

$\Rightarrow 12 = \frac{94 + x}{9}$

$\Rightarrow 12 \times 9 = 94 + x$

$\Rightarrow 108 = 94 + x \Rightarrow x = 108 - 94 = 14$

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