Final answer:
Adding the number 96 to a data set with a previous maximum of 84 increases the range by exactly 12 since the range is the difference between the maximum and minimum values of the data set.
Step-by-step explanation:
The student's question is concerned with how adding a new number to a data set of positive integers affects certain statistical measures. Specifically, when a value of 96 is added to a set where the previous maximum was 84, which measure will increase by exactly 12?
The correct answer is C. The range. The range is the difference between the maximum and minimum values in a data set. Adding a larger number increases the maximum value, thus increasing the range by the difference between the new maximum and the old maximum. If the original maximum was 84 and the new maximum is 96, the range will increase by 12 (96 - 84 = 12).
Options A (The mean), B (The median), and D (The standard deviation) will not necessarily increase by exactly 12. The mean will increase, but by an amount dependent on the sum of all the other numbers in the set. The median may or may not change, depending on the other values in the data set, but it will not specifically increase by 12. The standard deviation is a measure of spread from the mean and is influenced by each data point, so it will not specifically increase by 12 either.