If the mode of the following data is 7, then find the value of k.

2, 4, 6, 7, 5, 6, 10, 6, 7, 2k+1, 9, 7, 13

Correct option is A

Given:

We are given the data set:

$2,4,6,7,5,6,10,6,7,2k+1,9,7,13$

And the mode of this data is 7​

Concept Used:

The mode is the number that occurs the most frequently in a set of data.

Solution:

​Let's list the numbers and their frequencies:

2 occurs 1 time.

4 occurs 1 time.

6 occurs 3 times.

7 occurs 3 times.

5 occurs 1 time.

10 occurs 1 time.

2k + 1 occurs 1 time.

9 occurs 1 time.

13 occurs 1 time. 

So, 6 and 7 both appear 3 times. Since we are told that the mode is 7, it must appear more frequently than 6. Therefore, to make 7 the mode, the number $2k+1$ must be equal to 7.

​We now set the expression for $2k+1$ equal to 7:

​2k + 1 = 7

2k = 7 − 1

2k = 6 

​$$k =\frac{6}{2} = 3$$ 

The value of $k$ is 3.​