To find the interquartile range (IQR) of the dataset, we first need to determine the first quartile (Q1) and the third quartile (Q3).
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Arrange the data in ascending order: The dataset is already sorted: \(1, 2, 2, 4, 5, 6, 6, 8, 8\)
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Find Q1 (the first quartile): Q1 is the median of the first half of the data. The first half of the dataset, excluding the median, is \(1, 2, 2, 4\). For this half, there are four numbers. The median is calculated as follows: \[ Q1 = \frac{2 + 2}{2} = 2 \]
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Find Q3 (the third quartile): Q3 is the median of the second half of the data. The second half of the dataset, excluding the median, is \(6, 6, 8, 8\). For this half, the median is calculated as: \[ Q3 = \frac{6 + 8}{2} = 7 \]
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Calculate the interquartile range (IQR): The IQR is the difference between Q3 and Q1: \[ IQR = Q3 - Q1 = 7 - 2 = 5 \]
Thus, the interquartile range (IQR) of the dataset is 5.