Final answer:
To find the IQR, the data must first be sorted, then the first and third quartiles are identified, and finally the IQR is calculated by subtracting the first quartile from the third quartile; in this case, the IQR is 5.5.
Step-by-step explanation:
The student has provided a set of data representing the number of remote controllers each student owns. The first step is to sort the data from least to greatest: 0, 0, 1, 1, 2, 2, 4, 5, 7, 8.
Next, we calculate the first quartile (Q1), third quartile (Q3), and the interquartile range (IQR). With 10 data points, Q1 is the average of the 2.5th and 3rd data points (since we can't have a 2.5th data point, we take the average of the 2nd and 3rd), and similarly for Q3 (between the 7.5th and 8th data points).
Thus, Q1 is the average of 0 and 1, which is 0.5, and Q3 is the average of 5 and 7, which is 6. The IQR is Q3 minus Q1, so IQR = 6 - 0.5 = 5.5.