To find the interquartile range (IQR) of the dataset, we need to follow these steps:
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Organize the Data: The data provided is already in ascending order: \[ 8, 9, 9, 10, 12, 12, 13, 14, 15, 15, 15, 16, 18, 19, 20 \]
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Determine Quartiles:
- Q1 (First Quartile): This is the median of the first half of the data.
- Q2 (Median): This is the median of the entire dataset.
- Q3 (Third Quartile): This is the median of the second half of the data.
The dataset has 15 values, so:
- The median (Q2) is the 8th value: \[ Q2 = 14 \]
To find Q1, we take the first 7 values: \[ 8, 9, 9, 10, 12, 12, 13 \]
- The median of this subset (the 4th value) is: \[ Q1 = 10 \]
To find Q3, we take the last 7 values: \[ 15, 15, 15, 16, 18, 19, 20 \]
- The median of this subset (the 4th value) is: \[ Q3 = 16 \]
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Calculate the Interquartile Range (IQR): \[ \text{IQR} = Q3 - Q1 = 16 - 10 = 6 \]
So, the interquartile range of the data is 6.