You have a list of numbers. Someone asks for the "average." But which average — mean, median, or mode? They give different answers, and choosing the wrong one can mislead.
Here's how to calculate each one and when to use it.
The Three Measures of Central Tendency
| Measure | What It Is | Best For | |---------|-----------|----------| | Mean | Sum ÷ count | Symmetric data, no outliers | | Median | Middle value when sorted | Skewed data, outliers present | | Mode | Most frequent value | Categorical data, finding peaks |
Calculating the Mean
Mean = Sum of all values / Number of values
Example: Test scores 72, 85, 90, 65, 78
Mean = (72 + 85 + 90 + 65 + 78) / 5 = 390 / 5 = 78
Example: Salaries ₹25K, ₹30K, ₹35K, ₹200K
Mean = (25 + 30 + 35 + 200) / 4 = 290 / 4 = ₹72.5K
Notice: the ₹200K outlier pulls the mean way above what most people earn. The mean is misleading here.
Calculating the Median
- Sort the data
- If odd count: middle value
- If even count: average of two middle values
Example (odd): 72, 85, 90, 65, 78
Sorted: 65, 72, 78, 85, 90 → median = 78
Example (even): 12, 15, 18, 22, 25, 30
Sorted: 12, 15, 18, 22, 25, 30 → median = (18 + 22)/2 = 20
Example: Salaries ₹25K, ₹30K, ₹35K, ₹200K
Sorted: 25, 30, 35, 200 → median = (30 + 35)/2 = ₹32.5K
The median is much more representative than the mean (₹72.5K) when outliers exist.
Calculating the Mode
The mode is the most frequently occurring value.
Example: 3, 7, 7, 2, 5, 7, 9
Mode = 7 (appears 3 times)
Example: 2, 4, 6, 8
No mode — all values appear equally often
Example: 3, 3, 5, 5, 7
Bimodal — both 3 and 5 are modes (appear twice each)
When to Use Which Measure
| Situation | Use | Why | |-----------|-----|-----| | Exam scores (no outliers) | Mean | Sensitive to every score | | Income/salary data | Median | Resistant to outlier influence | | Favorite color survey | Mode | Categorical data — mean/median don't apply | | Home prices in an area | Median | A few mansions skew the mean | | Shoe size inventory | Mode | Stock the most demanded size | | Cricket scores | Mean | Average runs per innings |
The Trench Truth: News reports often cite "average income" without specifying mean or median. If they're using mean, a few billionaires make everyone look richer. If they're using median, you see what the typical person actually earns. Always check which average is being reported — it changes the story completely.
Try our statistics calculator to compute mean, median, mode, and more from any dataset.
Related: Standard Deviation Calculator · Derivative Calculator · Quadratic Formula Calculator
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