The upper and lower outer fences are specific boundaries calculated using the quartiles and the interquartile range (IQR) of a data set. These fences are commonly used to identify potential outliers within the data.
Understanding the Fences
According to the provided reference, the upper and lower fences are determined by a rule that utilizes the quartiles and IQR of a data set. Data points that fall beyond these calculated fences are considered outliers.
Formulas for the Fences
The calculation of the upper and lower fences relies on the first quartile (Q1), the third quartile (Q3), and the interquartile range (IQR).
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Interquartile Range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
IQR = Q3 - Q1
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Lower Fence: Calculated by subtracting 1.5 times the IQR from the first quartile (Q1).
- The formula for the lower fence is Q1 - 1.5(IQR).
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Upper Fence: Calculated by adding 1.5 times the IQR to the third quartile (Q3).
- The formula for the upper fence is Q3 + 1.5(IQR).
Identifying Outliers
A data point is considered an outlier if it is either below the lower fence or above the upper fence.
- If a data point
< Lower Fence, it is a potential outlier. - If a data point
> Upper Fence, it is a potential outlier.
Practical Application
Identifying these fences is a key step in exploratory data analysis, often performed before statistical modeling. It helps in understanding the spread of the data and detecting unusual observations that might require further investigation or treatment.
For example, if you have a dataset of house prices and calculate Q1, Q3, and the IQR, you can then compute the lower and upper fences. Any house price below the lower fence or above the upper fence might be considered an outlier – perhaps a fixer-upper or a luxury mansion skewing the data.
Summary Table:
| Term | Formula | Purpose |
|---|---|---|
| Lower Fence | Q1 - 1.5(IQR) |
Boundary for low outliers |
| Upper Fence | Q3 + 1.5(IQR) |
Boundary for high outliers |
Understanding these fences provides a standardized method for identifying data points that lie significantly far from the bulk of the data.
