Answer :
Final answer:
To ensure 15 remains the mode of the data set, x must be 15 because it allows 15 to be the most frequent number in the data set without being exceeded by others.
Explanation:
The question asks us to determine the value of x that will make 15 the mode of the given data set. The mode is the number that appears most frequently in a set of data. Given the data set 10,11,12,10,15,14,15,13,12,x,9,7 and knowing that 15 must be the mode, we look for the frequency of each number.
We can see that 15 appears twice in the provided data. For 15 to be the confirmed mode, x cannot be a number that appears more than twice; otherwise, it would become the new mode. Hence, the only number that can be chosen for x without changing the mode is 15, which also appears twice.
Therefore, the correct answer is B. 15, as choosing 15 for x will ensure that we have three instances of the number 15, confirming it as the mode of the dataset.
