Final answer:
To make Q1 of the data set equal to 11, the value of x must be 12. This was calculated by ordering the data set, determining the position of Q1 within it, and solving the equation that sets Q1 to the desired value.
Step-by-step explanation:
The student is asking how to find the value of x so that the first quartile (Q1) of a set of data is 11. To solve this, first we need to order the data set in ascending order and then find the position of Q1. Since Q1 is the median of the lower half of the data set, for an odd set of numbers, it will be the middle number. For an even set of numbers, it will be the average of the two middle numbers.
Now we arrange the data set given: 8, 10, 16, 25, 30, 35, 40, and we substitute the unknown number with x: 8, 10, x, 16, 25, 30, 35, 40. Since we have 8 numbers in the data set, Q1 will be the average of the 2nd and 3rd values when the set is ordered. We want Q1 to be 11, so we have (10 + x) / 2 = 11, therefore 10 + x = 22, which gives us x = 12.
Thus, the answer is A. 12.