If arithmetic mean of digits 3, 4, 8, 5, x, 3, 2, 1 is 4, then find x.

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Solution

Given : A.M. = 4
$∵ A . M . = \frac{S u m o f o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s}$
$= \frac{S u m o f d i g i t s}{N u m b e r o f d i g i t s}$
$\Rightarrow 4 = \frac{3 + 4 + 8 + 5 + x + 3 + 2 + 1}{8}$
$\Rightarrow 26 + x = 32$
$\Rightarrow x = 32 - 26 = 6$
Thus, $x = 6$

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