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

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

Options:

Correct Answer: 6

Solution:

Q1 = 3, Q3 = 9. IQR = Q3 - Q1 = 9 - 3 = 6.

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

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

Step 1: Arrange the data set in ascending order. The data set is already arranged: 1, 3, 5, 7, 9, 11, 13.
Step 2: Find the median of the data set. The median is the middle number. Since there are 7 numbers, the median is the 4th number, which is 7.
Step 3: Divide the data set into two halves. The lower half is 1, 3, 5, and the upper half is 9, 11, 13.
Step 4: Find Q1 (the first quartile) which is the median of the lower half. The lower half is 1, 3, 5. The median of this set is 3.
Step 5: Find Q3 (the third quartile) which is the median of the upper half. The upper half is 9, 11, 13. The median of this set is 11.
Step 6: Calculate the interquartile range (IQR) using the formula IQR = Q3 - Q1. Substitute the values: IQR = 11 - 3.
Step 7: Perform the subtraction: 11 - 3 = 8. Therefore, the IQR is 8.

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