Question

The mean of 5 numbers is 18, if one number is excluded, the mean is 16. Find the excluded number?

Answer 1

Hint: Assume a variable which will represent the number which is excluded. If we are given n numbers, the mean of these n numbers can be found by dividing the sum of these n numbers by n. Using this formula of mean, this question can be solved.

Complete step-by-step answer:

Before proceeding with the question, we must know the formula that will be required to solve this question.
If there are n numbers of which we are required to find the mean, then the mean can be found out by first finding the sum of these n numbers and then dividing this sum by n . . . . . . . . . (1)
In this question, it is given that the mean of 5 numbers is 18. Also, it is given that if one number is excluded, the mean is 16. We are required to find the excluded number.
Let us assume that the excluded number is x. Also, let us assume that the other four numbers are a, b, c, d.
It is given that the mean of 5 numbers is 18. So, using formula (1), we get,
$\begin{align}
  & \dfrac{a+b+c+d+x}{5}=18 \\
 & \Rightarrow a+b+c+d+x=18\times 5 \\
\end{align}$
$\Rightarrow a+b+c+d+x=90$ . . . . . . . . (2)
Also, it is given that when x is excluded, the mean of the other 4 numbers is 16. So, using formula (1), we get,
$\begin{align}
  & \dfrac{a+b+c+d}{4}=16 \\
 & \Rightarrow a+b+c+d=16\times 4 \\
\end{align}$
$\Rightarrow a+b+c+d=64$ . . . . . . . . (3)
Substituting equation (3) in equation (2), we get,
$64+x=90$
$\Rightarrow x=26$
Hence, the excluded number is 26.

Note: This is an easy question which requires a basic knowledge of statistics. But sometimes, in a hurry to solve these easy questions, we commit a mistake while doing calculations in such types of questions. So, one must be careful while doing calculations in such types of questions.