Question

The mean of 9, 14, x, 16, 7 and 18 is 11.5. Find the value of x.

Answer 1

Hint: We have given the mean of 9, 14, x, 16, 7 and 18 as 11.5. We know that the formula for mean is equal to $\dfrac{\text{Sum of observations}}{\text{Total number of observations}}$. The total number of observations given in the above problem is equal to 6 and their mean is 11.5 so substitute these values in the mean formula. And in place of the sum of observations write the addition of all the 6 observations. Simplify the expression and find the value of x.

Complete step by step answer:
We have given the mean of the following numbers as 11.5.
9, 14, x, 16, 7 and 18
We know the formula for mean of the observations as:
$Mean=\dfrac{\text{Sum of observations}}{\text{Total number of observations}}$
To put the value in total number of observations in the above formula, we have to count the numbers of observations given in the above problem. After counting them, we found that the number of observations is 6.
Now, to get the sum of 6 observations we are going to add all the 6 observations.
$9+14+x+16+7+18$
Substituting the above values in the formula of mean we get,
$\begin{align}
  & 11.5=\dfrac{9+14+x+16+7+18}{6} \\
 & \Rightarrow 11.5=\dfrac{64+x}{6} \\
\end{align}$
Cross multiplying the above equation we get,
$\begin{align}
  & 11.5\left( 6 \right)=64+x \\
 & \Rightarrow 69.0=64+x \\
 & \Rightarrow x=5 \\
\end{align}$
From the above solution, we got the value of x as 5.

Hence, the value of x in the given observations is 5.

Note: You can check the value of x that you are getting is correct or not by substituting the value of x as 5 in the given observations and then find the mean of these 6 observations.
Adding the 6 numbers given in the above problem as:
$\begin{align}
  & 9+14+5+16+7+18 \\
 & =69 \\
\end{align}$
Now, dividing the above result to 6 we get the mean of these 6 observations.
$\dfrac{69}{6}=11.5$
In the above problem, we have given the value of the mean of 6 observations as 11.5 and the above result is matching with our result. Hence, we have found the right value of x.