If the median of data $31, 33, 35, x, x + 10, 48, 48, 50$ is $40$ than find the value of $x$ .

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Solution

$31, 33, 35, x, x + 10, 48, 48, 50$
Given data
Number of observations $= 8$
Median $= \frac{v a l u e o f (\frac{8}{2}) o b s + v a l u e o f (\frac{8}{2} + 1) o b s}{2}$
i.e. $\frac{v a l u e o f 4^{t h} o b s + v a l u e o f 5^{t h}}{2}$
$= \frac{x + x + 10}{2} = x + 5$
Given $x + 5 = 40$
i.e. $x = 35$

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