If the mode of the following data is 7, then the value of k in the data set 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k+5, 9, 7, and 13 is:a.1b.3c.4d.7

To find the value of k in the given data set, we need to determine the value that satisfies the condition that the mode of the data is 7.

The mode is the value that appears most frequently in the data set. In this case, the mode is 7.

Looking at the data set, we see that the number 7 appears three times.

Now, we need to find the value of k that makes the number 7 appear three times in the data set.

We can start by substituting the given data into the equation 2k+5 = 7.

Simplifying the equation, we have 2k = 2.

Dividing both sides of the equation by 2, we find that k = 1.

Therefore, the value of k in the data set is 1.

So, the correct answer is a. 1.