To calculate the interquartile range (IQR) of the dataset \(1, 1, 3, 5, 9\), we first need to find the first quartile (Q1) and the third quartile (Q3):
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Order the data (already in order): \(1, 1, 3, 5, 9\)
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Find Q1 (the median of the first half):
- The first half of the data is \(1, 1\).
- Q1 = median of \(1, 1\) = \(1\)
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Find Q3 (the median of the second half):
- The second half of the data is \(3, 5, 9\).
- Q3 = median of \(3, 5, 9\) = \(5\)
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Calculate the interquartile range (IQR): \[ \text{IQR} = Q3 - Q1 = 5 - 1 = 4 \]
Thus, the interquartile range is \(4\).