What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?

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Question: What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?

Options:

Correct Answer: 6

Solution:

Q1 = 3, Q3 = 8. IQR = Q3 - Q1 = 8 - 3 = 5.

What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?

What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?

Step 1: Arrange the data set in ascending order. The data set is already arranged: {1, 3, 7, 8, 9}.
Step 2: Find the median of the data set. The median is the middle number. For {1, 3, 7, 8, 9}, the median is 7.
Step 3: Divide the data set into two halves. The lower half is {1, 3} and the upper half is {8, 9}.
Step 4: Find Q1 (the first quartile) which is the median of the lower half {1, 3}. The median of {1, 3} is 3.
Step 5: Find Q3 (the third quartile) which is the median of the upper half {8, 9}. The median of {8, 9} is 8.
Step 6: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. Substitute the values: IQR = 8 - 3.
Step 7: Perform the subtraction: 8 - 3 = 5. Therefore, the IQR is 5.

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