Question

The data representing the age of $5$ participants is given as follows:


The difference between their mode and mean age is .

Answer 1

The mean age of the participants can be calculated as,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{24+26+28+28+29}{5}\\ & =\frac{135}{5}\\ & =27\end{array}$

Thus, their mean age is $27$.

Observe the given data,


Here, the most frequently occuring value is $28$, thus the mode of their ages is $28$.

Hence, the required difference between the mode and mean age is,

$\begin{array}{cc}\text{Difference}& =\text{Mode age}-\text{Mean age}\\ & =28-27\\ & =1\end{array}$