Question

If the arithmetic mean of \[8,4,6,x,2,7\] is $5$, then find the value of $x$.

Answer 1

Hint: Here for answering question of this type the arithmetic mean of $n$ numbers is found by using the mathematical formula given by$\dfrac{\sum\limits_{i=1}^{n}{{{a}_{i}}}}{n}$ . We have the arithmetic mean and the 5 numbers given in the question. The total number of numbers present is 6 this implies that $n=6$. The remaining value will be found after simplifying the calculations.

Complete step-by-step answer:
 It is given in the question that the arithmetic mean of \[8,4,6,x,2,7\] is$5$. Since the arithmetic mean of $n$ numbers is found by using the mathematical formula given by $\dfrac{\sum\limits_{i=1}^{n}{{{a}_{i}}}}{n}$ .
Hence we can say that mathematically $5=\dfrac{8+4+6+x+2+7}{6}$ .
By performing addition of all the values we will have, $5=\dfrac{27+x}{6}$ .
By taking 6 on the L.H.S from the R.H.S we will have, $5\times 6=27+x$ .
By performing multiplication in the L.H.S we will have $30=27+x$ .
By taking all the numbers on the L.H.S from the R.H.S we will have $30-27=x$ .
By performing subtraction for the numbers on the L.H.S we will have $3=x$ .
This gives us the value of $x$ as 3. Hence the answer is 3.
So we conclude that the value of $x$ is 3 mathematically can be given as $x=3$ .

Note: While answering questions of this type we should perform the calculations carefully. If we perform a wrong calculation such as $5=\dfrac{8+4+6+x+2+7}{6}\Rightarrow 5=\dfrac{24+x}{6}$. After simplifying step by step we will have $5\times 6=24+x\Rightarrow 30=24+x\Rightarrow 30-24=x\Rightarrow 6=x$ .We will end up with a wrong conclusion that the value of $x$ is 6.