Question

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

Answer 1

Hint: Mean is a statistical value which is the average of the given data, or can be also defined as the ratio of the sum of the number of the given statistical values and the total number of values. Mean is simply called as the average of the collected samples in the given data values. In statistics the mean and average are the same, which is the ratio of summation of the values observations to the total number of observations.

Complete step-by-step solution:
In general the arithmetic mean of n observations in given data is given by:
$ \Rightarrow {x_n} = \dfrac{{\sum\limits_i {{x_i}} }}{n}$
$ \Rightarrow \dfrac{{\sum\limits_i {{x_i}} }}{n} = \dfrac{{{x_1} + {x_2} + {x_3} + \cdot \cdot \cdot \cdot + {x_n}}}{n}$
Given the data, values of the data, the total number of values are 5 , and also given the mean, we have to find the value of x :
$ \Rightarrow {x_n} = \dfrac{{x + (x + 2) + (x + 4) + (x + 6) + (x + 8)}}{5}$
Here the mean ${x_n} = 11$, hence substituting in the mean expression to get the value of x:
$ \Rightarrow \dfrac{{x + (x + 2) + (x + 4) + (x + 6) + (x + 8)}}{5} = 11$
$ \Rightarrow \dfrac{{5x + 20}}{5} = 11$
$ \Rightarrow 5x + 20 = 55$
$ \Rightarrow 5x = 35$
$ \Rightarrow x = 7$
$\therefore $ The value of $x = 7.$

The value of x is 7.

Note: Here we used the general arithmetic mean formula to find the value of an unknown variable, given already the value of the arithmetic mean. It is always important to remember that to consider the correct number of total observations, as it plays a major role in finding the mean.