What is an outlier in a dataset?
Conditions
- Applies to any dataset with records, observations, samples, or data points.
Reasoning, step by step
- Observe the dataset or plot.
- Identify the main cluster of data points.
- Locate any point that lies far away from this cluster.
- Classify that isolated point as an outlier.
Example
In the student marks example, the scores are 15, 20, 25, 20, and 100. The score 100 is an outlier because it is extremely different from the other four scores.
Common misconceptions
- Assuming outliers are always errors; they can be valid extreme observations.
- Thinking outliers are only high values; they can also be unusually low values.
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Related questions
Replacing an outlier with a typical value removes the extreme inflation from the sum of the dataset. This causes the arithmetic mean to drop significantly, reflecting the true central tendency of the majority of the data.
Conditions: The original dataset contains an outlier.; The replacement value is consistent with the majority of the data.; The sample size remains unchanged.
A model attempts to fit the overall trend of the data. When an outlier is present, the fitting algorithm tries to minimize the error across all points, including the extreme one.
Conditions: The data can be represented as a two-dimensional scatter plot.; The model attempts to fit the overall trend.; There exist observations clearly distant from the main cluster.
The decision rule is based on comparing the class average to a fixed threshold. An outlier artificially inflates the average above the threshold, preventing the class from receiving help.
Conditions: The decision rule is: hold extra classes only if the average score is below 35.; The dataset contains an outlier.; The threshold is fixed at 35.
The arithmetic mean is sensitive to outliers. A single extreme score can pull the overall average above the threshold, masking the fact that the majority of individual scores are still below the threshold and require additional help.
Conditions: The decision rule relies solely on the class average score.; The dataset contains a significant outlier.; The threshold is set at 35.
In a scatter plot, outliers are identified as individual data points that lie far away from the main cluster of points. They are spatially separated from the majority of the data and often deviate significantly from the general trend or regression line.
Conditions: A two-dimensional coordinate system and a set of data points are present.; The data points form a recognizable main cluster.
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