An outlier in a dataset is a value that significantly differs from other observations. Such anomalies can arise due to errors in measurement or experimentation, or when the data comes from a population with a long-tailed distribution.

To identify outliers using the quartile method, follow these steps:

**Sort the Data**: Arrange the data points in ascending order. For example, consider the dataset {4, 5, 2, 3, 15, 3, 3, 5}. Sorted, it becomes {2, 3, 3, 3, 4, 5, 5, 15}.**Find the Median (Q2)**: Determine the median, which is the middle value in the sorted dataset. If there’s an even number of data points, average the two middle values. In our example, the median is (3 + 4) / 2 = 3.5.**Find the Upper Quartile (Q3)**: Locate the value at which 25% of the data points are larger. If the dataset size is even, average the two points around the quartile. In the example, Q3 = (5 + 5) / 2 = 5.**Find the Lower Quartile (Q1)**: Identify the value at which 25% of the data points are smaller. If even, average the two points around the quartile. For the example, Q1 = (3 + 3) / 2 = 3.**Calculate the Interquartile Range (IQR)**: Subtract the lower quartile (Q1) from the upper quartile (Q3). In our example, IQR = Q3 – Q1 = 5 – 3 = 2.**Identify Mild Outliers**: Multiply the IQR by 1.5. Add the result to Q3 and subtract it from Q1 to establish the mild outlier boundaries. For the example, 1.5 x 2 = 3. So, Q1 – 3 = 0 and Q3 + 3 = 8. Any value less than 0 or greater than 8 is considered a mild outlier.**Identify Extreme Outliers**: Multiply the IQR by 3 to determine the boundaries for extreme outliers. For the example, 3 x 2 = 6. Thus, Q1 – 6 = -3 and Q3 + 6 = 11. Any value less than -3 or greater than 11 is classified as an extreme outlier.

In our example dataset, the value 15 qualifies as both a mild and extreme outlier based on these calculations. Identifying and possibly removing outliers from a dataset can help ensure that statistical analyses accurately reflect the characteristics of the sample population.

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