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# The mean and median of a data are $14$ and $15$ respectively. The value of mode is$\left( a \right){\text{ 16}}$$\left( b \right){\text{ 17}}$$\left( c \right){\text{ 13}}$$\left( d \right){\text{ 18}}$

Last updated date: 20th Jun 2024
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Hint: In this question we have the values of mean and the median given. We have to find the mode. So for this there is a relation between these three and it is given by $Mode = {\text{3 median - 2 mean}}$ . And is also known to be an empirical formula. So on substituting the values and equating we will get the value for the mode.

Formula used:
The relation between the mean, median and mode is given by
$Mode = {\text{3 median - 2 mean}}$

First of all we will see the values given to us. Here in this question we have the value for the mean and median. And it is given by $14$ and $15$ respectively.
Now by using the relation, we have the relation as $Mode = {\text{3 median - 2 mean}}$
$\Rightarrow Mode = 3 \times 15 - 2 \times 14$
$\Rightarrow Mode = 45 - 28$
$\Rightarrow Mode = 17$
Therefore, the value of the mode will be equal to $17$
Hence, the option $\left( b \right)$ is correct.