Question

If mode of the following data is $7$, then the value of $k$ in the $2,4,6,7,5,6,10,6,7,2k+1,9,7,13$ is:

• A. $3$
• B. $7$
• C. $4$
• D. $2$

Answer 1

The correct option is A $3$

Mode is the value which occurs most often in the data set of values.

Given data values are $2,4,6,7,5,6,10,6,7,2k+1,9,7,13$

In the above data set, values $6,7$ have occured more times i.e., 3 times

But given that mode is $7$. So, should occur more times than $6$. Hence the variable $2k+1$ must be 7

$⟹2k+1=7$

$⟹2k=6⟹k=\frac{6}{2}$

$⟹k=3$