To find the interquartile range (IQR) of Ezra's passenger data, we first need to determine the quartiles of the dataset. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
Step 1: Organize the data
The data provided is already in ascending order: 8, 9, 9, 10, 12, 12, 13, 14, 15, 15, 15, 16, 18, 19, 20.
Step 2: Find Q1 (the first quartile)
Since there are 15 data points, the median (Q2) is the 8th number: 14.
The first half of the data (for Q1) is: 8, 9, 9, 10, 12, 12, 13. The median of this subset (the 4th number) is 10 , meaning Q1 is 12.
Step 3: Find Q3 (the third quartile)
The second half of the data (for Q3) is: 15, 15, 15, 16, 18, 19, 20. The median of this subset (the 4th number) is 16, so Q3 is 16.
Step 4: Calculate the IQR
The interquartile range is calculated as: IQR = Q3 - Q1
IQR = 16 - 12 = 4.
Final Answer
The interquartile range (IQR) of Ezra's passenger data is 4.