What is Outlier?

🔎 Introduction

In statistics, an outlier is a data point that lies far away from the rest of the observations. Outliers can distort averages, inflate variances, and sometimes reveal interesting hidden patterns.

📘 Definition of Outlier

An outlier is an observation that deviates significantly from the other values in a dataset. It may be caused by measurement error, unusual experimental conditions, or genuine variability.

⚠️ Why Are Outliers Important?

They can influence mean and standard deviation, giving misleading results.
They may indicate errors in data collection.
Sometimes they represent rare but important events (e.g., fraud detection, anomalies).

🛠 Methods to Detect Outliers

1. Z-Score Method

A data point is considered an outlier if its Z-score is very high (commonly greater than 3 in absolute value):

$$ Z = \frac{x - \bar{x}}{s} $$

where $\bar{x}$ is the mean and $s$ is the standard deviation.

2. Interquartile Range (IQR) Rule

Compute quartiles $Q_1$ and $Q_3$, then the interquartile range:

$$ IQR = Q_3 - Q_1 $$

An observation is an outlier if it lies below $Q_1 - 1.5 \times IQR$ or above $Q_3 + 1.5 \times IQR$.

3. Boxplot Visualization

A boxplot is a simple way to visualize outliers. Points outside the whiskers are potential outliers.

**Figure 1:** Boxplot with outliers shown as individual points beyond the whiskers.

📊 Example

Suppose we have exam scores: 45, 48, 50, 52, 55, 57, 95.

The score 95 lies much higher than the rest.
Z-score method: $Z \approx 3.2$, so it is an outlier.
IQR method: 95 > $Q_3 + 1.5 \times IQR$, so it is also flagged as an outlier.

🛠 Handling Outliers

Investigate whether it is a data entry or measurement error.
If genuine, decide whether to keep or remove it, depending on study goals.
Sometimes use robust statistics (median, IQR) instead of mean & variance.

📝 Key Takeaways

Outliers are observations that deviate significantly from the rest of the data.
They affect mean, variance, and regression results.
Detection methods include Z-scores, IQR rule, and boxplots.
Always investigate outliers before deciding to remove them.

👉 Related Posts

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Saturday, June 2, 2018