Question

Consider the following set of numbers,


If the mean of this data is known to be $4.8$, then what will be the mode of this data set, if any?

• A. $4$
• B. $8$
• C. $2$
• D. No mode

Answer 1

The correct option is A $4$

The mean of the given data set is $4.8$. Use the formula of mean to calculate the vale of $x$.

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ 4.8& =\frac{4+8+x+6+2}{5}\\ 4.8\times 5& =20+x\\ 24-20& =x\\ 4& =x\end{array}$

Thus, the given data set will be represented as,


Here, it can be observed that $4$ occurs most frequently, thus the mode of the given set of numbers is $4$.

So, option (a) is correct.