Question

If the mean of 24, 28, 32, 36, $x$ is 32. Then find $x$.
(a) 40
(b) 36
(c) 32
(d) zero

Answer 1

Hint: In this question, first we will write down all the given information and then figure out a method to solve the problem. We will use the formula of mean, Mean $\left( \mu \right)$$=\dfrac{\text{sum of the terms}}{\text{number of terms}}$ to solve the problem by substituting the given values and finding the value of $x$ also the fifth term in the series.

Complete step by step answer:
Here in this question, we have been given the mean 32 of 5 numbers which are 24, 28, 32, 36 and $x$, now using the mean and the other four numbers we need to find the fifth number.
We will use the formula of the mean to find the fifth number, hence we know the mean is basically the ratio of sum of the terms to the total number of terms.
We get,
Mean $\left( \mu \right)$$=\dfrac{\text{sum of the terms}}{\text{number of terms}}$
Let us substitute the given data in the above mean formula, we get
               $32=\dfrac{24+28+32+36+x}{5}$
Now, if we add the numbers in the numerator and multiply by 5 on both the sides, we get
\[\begin{align}
  & 32\times 5=\dfrac{120+x}{5}\times 5 \\
 & 160=120+x
\end{align}\]
We will now subtract both the sides by 120 and solve, we will get
$160-120=120+x-120$
             $40=x$
Now, the value of the fifth term is 40.
Hence, the value of $x$ is equal to 40.


Note:
There are different types of mean, for example, the one we used to solve the problem is the arithmetic mean (AM). The other types are geometric mean (GM), harmonic mean (HM), weighted mean. The relation between AM, GM and HM is given by $\text{AM}\ge \text{GM}\ge \text{HM}$. Mean is also termed as average. Mean is basically a part of the statistics, if a set of data is given, we can calculate the mean, median and mode.