To calculate the interquartile range (IQR) of the given data set, we first need to find the first quartile (Q1) and the third quartile (Q3).
The data set is:
2, 3, 3, 5, 7, 7, 9, 9
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Order the data (already ordered in this case): 2, 3, 3, 5, 7, 7, 9, 9
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Find Q1 (the first quartile): Q1 is the median of the first half of the data. The first half is: 2, 3, 3, 5
The median of this half (Q1) is the average of the two middle numbers (3 and 3): \[ Q1 = \frac{3 + 3}{2} = 3 \]
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Find Q3 (the third quartile): Q3 is the median of the second half of the data. The second half is: 7, 7, 9, 9
The median of this half (Q3) is the average of the two middle numbers (7 and 9): \[ Q3 = \frac{7 + 9}{2} = 8 \]
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Calculate the IQR: The interquartile range (IQR) is calculated as: \[ IQR = Q3 - Q1 = 8 - 3 = 5 \]
Thus, the interquartile range of the data set is 5.