To identify outliers in a skewed dataset, we typically use the interquartile range (IQR) method. Here are the steps to determine the quartiles and outliers for the dataset: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.
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Order the dataset: The dataset is already ordered.
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Find the quartiles:
- First Quartile (Q1): The median of the first half of the data (5, 6, 6, 7, 7, 8). The median is 7.
- Third Quartile (Q3): The median of the second half of the data (8, 8, 9, 9, 14, 16). The median is 9.5.
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Calculate the IQR:
- IQR = Q3 - Q1 = 9.5 - 7 = 2.5.
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Determine the lower and upper bounds:
- Lower Bound = Q1 - 1.5 * IQR = 7 - 1.5 * 2.5 = 7 - 3.75 = 3.25.
- Upper Bound = Q3 + 1.5 * IQR = 9.5 + 1.5 * 2.5 = 9.5 + 3.75 = 13.25.
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Identify outliers:
- Any data point below 3.25 or above 13.25 is considered an outlier.
- In the dataset, values 14 and 16 are greater than 13.25, so they are outliers.
Based on this analysis, the correct response is:
The outliers of the dataset are 14 and 16.