What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?

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Q: What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?

Solution: Q1 = 4, Q3 = 10. IQR = Q3 - Q1 = 10 - 4 = 6.

Steps: 6

Step 1: Arrange the data set in ascending order. The data set is already arranged: {1, 3, 5, 7, 9, 11, 13, 15}.
Step 2: Find the median of the data set. Since there are 8 numbers (even), the median is the average of the 4th and 5th numbers: (7 + 9) / 2 = 8.
Step 3: Divide the data set into two halves. The lower half is {1, 3, 5, 7} and the upper half is {9, 11, 13, 15}.
Step 4: Find Q1 (the median of the lower half). The lower half has 4 numbers, so Q1 is the average of the 2nd and 3rd numbers: (3 + 5) / 2 = 4.
Step 5: Find Q3 (the median of the upper half). The upper half has 4 numbers, so Q3 is the average of the 2nd and 3rd numbers: (11 + 13) / 2 = 12.
Step 6: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. Substitute the values: IQR = 12 - 4 = 8.