Distributions, Percentiles, and Outliers

What is a distribution?

A distribution shows how values are spread across their possible range.

The normal distribution is a common symmetric, bell-shaped reference. For data that is approximately normal:

Many business metrics are not normally distributed, so check the shape with a histogram before assuming this.

Percentiles and quartiles

Business use: "90% of deliveries arrive within 42 minutes" (P90) is often more useful than an average, because it describes the experience of most customers.

Identifying potential outliers

IQR rule (common screening rule):

• Lower fence = Q1 − 1.5 × IQR
• Upper fence = Q3 + 1.5 × IQR
• Values outside the fences are flagged as potential outliers.

Other approaches:

• Z-score: flags values more than ~3 SD from the mean (best for roughly normal data)
• Box plots: show the fences and flagged points visually
• Domain rules: e.g., "delivery time over 6 hours is impossible for this service"

A flag is a screening rule, not proof that a record is wrong. A high-value transaction may be unusual but legitimate.

Example

Most delivery times are 20–45 minutes, but one is 300 minutes. Investigate:

Do not remove it until you understand what it means.

Common mistakes

• Automatically deleting outliers. They may be the most important records, such as fraud, VIP customers, or failures.
• Not reporting the impact. Show results with and without outliers when relevant.
• Not documenting the rule used to flag or handle outliers.
• Applying z-scores to heavily skewed data.