Mean, Median, Mode: The Complete Guide to Calculating Averages

Understanding averages is fundamental to making sense of data — whether you’re calculating grades, analysing survey results, or tracking investment returns.

What is an average?

An average represents the central tendency of a dataset — a single number that summarises the whole group. But “average” isn’t just one thing. There are several types, each useful in different situations.

Types of averages

Arithmetic Mean

The most common average. Add all values and divide by count.

Mean = (x₁ + x₂ + ... + xₙ) ÷ n

Example: Exam scores 85, 90, 78, 92, 88 Mean = (85+90+78+92+88) ÷ 5 = 433 ÷ 5 = 86.6

Median

The middle value when numbers are sorted. Unaffected by outliers.

For {3, 7, 9, 12, 15}: Median = 9 (middle value) For {3, 7, 9, 12}: Median = (7+9)÷2 = 8 (average of two middle values)

Mode

The most frequently occurring value. A dataset can have multiple modes or no mode at all.

For {4, 7, 7, 9, 12}: Mode = 7

When to use each

Type	Use when…
Mean	Data is symmetric, no extreme outliers
Median	Data has outliers (salaries, house prices)
Mode	Finding most popular/common category
Weighted avg	Items have different importance (grades, portfolios)
Geometric mean	Growth rates, investment returns

Weighted average example

Your course grades with different credit weights:

• Maths (4 credits): 85
• English (3 credits): 92
• Physics (4 credits): 78
• History (2 credits): 90

Weighted Average = (85×4 + 92×3 + 78×4 + 90×2) ÷ (4+3+4+2) = 1108 ÷ 13 = 85.2

Common mistakes

1. Using mean with outliers — If one person earns ₹50 lakh in a group averaging ₹5 lakh, the mean is misleading. Use median instead.
2. Forgetting weights — In GPA calculations, a 4-credit course matters more than a 2-credit one.
3. Confusing sample vs population std deviation — Use n-1 for samples, n for full population.

Try our Average Calculator for instant mean, median, mode, weighted average, and standard deviation calculations.