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Question

If the mean of $$5$$ observations $$x, x+2, x+4, x+6$$ and $$x+8$$ is $$11$$, find the value of $$x$$.


Solution

We know that,
Mean $$=\dfrac {Sum\ of\ the\ given\ observation}{Total\ number\ of\ observation}$$
Sum of the given observations $$=x+(x+2)+(x+4)+(x+6)+(x+8)$$
$$=x+x+2+x+4+x+6+x+8$$
$$=5x+20$$
Total number of observations $$=5$$
Therefore, Mean $$=\dfrac{(5x+20)}{5}$$
Also, Mean $$=11$$
(given) 
$$\Rightarrow 11=\dfrac{(5x+20)}{5}$$
$$\Rightarrow 55=5x+20$$
or $$x=7$$

Mathematics
RS Agarwal
Standard X

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