To determine the outliers in the provided skewed dataset \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\), we can use the Interquartile Range (IQR) method.
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Calculate the Quartiles:
- Sort the data: \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\)
- The median (Q2) is the average of the 6th and 7th values: \((8 + 8) / 2 = 8\).
- Lower half: \(5, 6, 6, 7, 7, 8\); Q1 (Median of lower half) is \((6 + 7) / 2 = 6.5\).
- Upper half: \(8, 8, 9, 9, 14, 16\); Q3 (Median of upper half) is \((9 + 9) / 2 = 9\).
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Calculate IQR: \[ IQR = Q3 - Q1 = 9 - 6.5 = 2.5 \]
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Determine Outlier Boundaries: \[ \text{Lower Bound} = Q1 - 1.5 \cdot IQR = 6.5 - 1.5 \cdot 2.5 = 6.5 - 3.75 = 2.75 \] \[ \text{Upper Bound} = Q3 + 1.5 \cdot IQR = 9 + 1.5 \cdot 2.5 = 9 + 3.75 = 12.75 \]
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Identify Outliers:
- Any value below \(2.75\) or above \(12.75\) is an outlier.
- In your dataset, \(14\) and \(16\) are above \(12.75\) and are therefore outliers.
Thus, the correct response is:
The outliers of the dataset are 14 and 16.