Average, Median, Mode & Range: Complete Statistics Guide

Whether you're analyzing test scores, tracking expenses, or understanding data trends, knowing how to calculate and interpret average, median, mode, and range is essential. This guide explains all four measures with clear examples and when to use each.

1. Average (Mean)

The average (or mean) is the sum of all values divided by how many values there are.

Average = Sum of all values ÷ Count of values

When to Use Average

• When you want a general "typical" value
• When data has no extreme outliers
• For calculating GPA, average salary, average temperature

When NOT to Use Average

• When data has extreme outliers (use median instead)
• Example: Salaries [30K, 32K, 35K, 28K, 500K] → Average = 125K (misleading!)

2. Median

The median is the middle value when data is sorted from smallest to largest.

Steps:

1. Sort the numbers from smallest to largest
2. If odd count: middle number is the median
3. If even count: average of the two middle numbers

When to Use Median

• When data has extreme values (outliers)
• For income/salary data (not skewed by billionaires!)
• For house prices in a neighborhood

3. Mode

The mode is the value that appears most frequently.

Special Cases

• No mode: All values appear equally (e.g., [1, 2, 3, 4, 5])
• Bimodal: Two values tie for most frequent (e.g., [1, 1, 2, 2, 3])
• Multimodal: Three or more values tie

When to Use Mode

• For categorical data (favorite color, most popular product)
• When you want the "most common" value
• Inventory management (which size sells most?)

4. Range

The range shows the spread of data—how far apart the highest and lowest values are.

Range = Maximum value − Minimum value

When to Use Range

• To understand data variability
• Quality control (acceptable product variation)
• Weather forecasting (temperature swing)

Complete Example: All Four Measures

Which Measure Should You Use?

Real-World Applications

1. Sports Statistics

Cricket batting average: Total runs ÷ number of innings = average runs per match

2. Business Analytics

Median customer spend: Better than average (not skewed by one big purchase)

3. Education

Class average: Sum of all scores ÷ number of students

Median score: Middle score (shows where most students fall)

4. Finance

Average monthly expense: Total yearly expenses ÷ 12

Common Mistakes to Avoid

Mistake 1: Forgetting to Sort for Median

Wrong: [5, 3, 9, 7, 2] → median = 9 (middle of unsorted)

Right: Sort first [2, 3, 5, 7, 9] → median = 5

Mistake 2: Using Average with Outliers

Salaries: [30K, 32K, 35K, 28K, 500K]

Average = 125K (misleading!)

Median = 32K (better representation)

Mistake 3: Confusing Mode with Median

Mode = most frequent. Median = middle value. Completely different!

Practice Problems

1. Find average, median, mode, range: [12, 15, 12, 18, 20, 12, 14]
2. Why is median better than average for house prices?
3. Dataset: [2, 4, 6, 8, 10]. Calculate all four measures.

Answers:

1) Avg=14.7, Median=14, Mode=12, Range=8

2) Outliers (expensive mansions) skew the average upward

3) Avg=6, Median=6, Mode=None, Range=8