Outlier Detection Statistics Example 1

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Example 1

easy
The data set is: 10, 12, 11, 13, 12, 14, 11, 50. Identify the outlier and explain how you know.

Solution

  1. 1
    Step 1: Most values cluster between 10 and 14. The value 50 is far removed from this cluster.
  2. 2
    Step 2: Check with quartiles: Sort: 10,11,11,12,12,13,14,50. Q1=11Q_1 = 11, Q3=13.5Q_3 = 13.5, IQR=2.5IQR = 2.5.
  3. 3
    Step 3: Upper fence: Q3+1.5×IQR=13.5+3.75=17.25Q_3 + 1.5 \times IQR = 13.5 + 3.75 = 17.25. Since 50 > 17.25, it is a confirmed outlier by the 1.5×IQR1.5 \times IQR rule.

Answer

The value 50 is an outlier. It exceeds the upper fence of 17.25 (using the 1.5×IQR1.5 \times IQR rule).
Outliers are data points that are significantly different from other observations. The 1.5×IQR1.5 \times IQR rule provides an objective method for identifying them: any value below Q1−1.5×IQRQ_1 - 1.5 \times IQR or above Q3+1.5×IQRQ_3 + 1.5 \times IQR is classified as an outlier.

About Outlier Detection

Outlier detection is the process of identifying data points that are unusually far from the rest of the dataset, using techniques like the IQR rule, z-scores, or visual inspection of box plots and scatter plots. These anomalous values may indicate measurement errors, data entry mistakes, or genuinely extreme observations.

Learn more about Outlier Detection →

More Outlier Detection Examples

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Example 4 hard

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