Outlier Detection Using the IQR Method

The 1.5 × IQR rule

An observation is an outlier if it falls below $Q1 - 1.5 \times IQR$ or above $Q3 + 1.5 \times IQR$.

Step-by-step: {3, 5, 7, 8, 9, 10, 45}

Step 1 — Sort: Already sorted. $n = 7$.

Step 2 — Quartiles: Q1 = 5, Median = 8, Q3 = 10.

Step 3 — IQR: $Q3 - Q1 = 10 - 5 = 5$.

Step 4 — Fences:

• Lower: $Q1 - 1.5(5) = 5 - 7.5 = -2.5$
• Upper: $Q3 + 1.5(5) = 10 + 7.5 = 17.5$

Step 5 — Check: Is 45 > 17.5? Yes! 45 is an outlier. All other values are between -2.5 and 17.5.

Why detect outliers?

Outliers can be: data entry errors, measurement errors, or genuine extreme values. They can distort the mean and standard deviation. Always investigate before removing.

Try it in the visualization

The box plot shows the IQR and fences. Values beyond the fences are flagged as outliers (red dots). Drag the outlier value to see the fences adjust.