Average Calculator
Calculate mean, median, mode, range and standard deviation for any set of numbers
Results & Details
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Statistical Measures Explained
Different types of "average" tell you different things about a dataset. No single measure is always best — the right choice depends on the nature of your data and what question you're trying to answer.
Formulas
Mean vs Median — When to Use Each
The mean is sensitive to outliers. A single very high or low value can pull it significantly. The median is resistant to outliers — it's a better measure of central tendency for skewed data like incomes, house prices or response times.
Example: Five salaries of £25k, £28k, £30k, £32k, £200k. Mean = £63k (misleading). Median = £30k (more representative).
Population vs Sample Std Deviation
Use population std deviation (σ) when you have data for every member of the group. Use sample std deviation (s) when your data is a sample drawn from a larger population — it uses n−1 in the denominator (Bessel's correction) to give an unbiased estimate.
Mean, Median, Mode and Standard Deviation — When Each One Lies
Built and verified by Andrius R. · Updated June 2026
"Average" sounds like one concept; statistics gives you three, plus a fourth number that says how much to trust them. Choosing the wrong one isn't a technicality — it's how honest data tells dishonest stories.
The classic demonstration: one outlier, two truths
$32,000 · $35,000 · $38,000 · $41,000 · $44,000 · $47,000 · $52,000 · $250,000 (the owner)
Mean: $67,375 — higher than what 7 of 8 people earn.
Median: $42,500 — what the typical person actually makes.
Both are "the average." A recruiter quotes the mean; an employee experiences the median. This is exactly why house prices, incomes and wealth are reported as medians: skewed data with big outliers drags the mean toward the extreme, while the median stays anchored to the middle person. Rule of thumb: roughly symmetric data → mean; skewed data or outliers → median.
All four measures on one dataset
For the values 4, 8, 6, 5, 3, 7, 9, 6:
| Measure | How | Result |
|---|---|---|
| Mean | sum ÷ count = 48 ÷ 8 | 6 |
| Median | middle of sorted list (avg of 6 and 6) | 6 |
| Mode | most frequent value | 6 |
| Standard deviation | spread around the mean | ~1.87 (population) / 2.0 (sample) |
When all three averages agree, the data is symmetric and the mean is safe. The mode earns its keep with categorical data — the best-selling shoe size is a mode question; a "mean shoe size of 8.37" helps nobody stock a shop.
Standard deviation: the trust rating
Two classes can both average 70% on a test — one with everyone between 65 and 75 (small SD), one with half scoring 40 and half scoring 100 (huge SD). Same mean, completely different stories. SD measures typical distance from the mean; for bell-shaped data, ~68% of values fall within 1 SD of the mean and ~95% within 2 — which is why "two standard deviations" is the everyday boundary for calling something unusual. Note the calculator's two versions: population SD (divide by n) when you have all the data, sample SD (divide by n−1) when your data is a sample standing in for something bigger — the n−1 corrects the sample's tendency to underestimate spread.
Averages that need special handling
- Averaging averages is usually wrong. A 90% score on a 10-question quiz and 60% on a 100-question exam don't average to 75% overall — weight by size: (9 + 60) ÷ 110 ≈ 62.7%.
- Rates and speeds need the harmonic view. Driving somewhere at 30 km/h and back at 60 km/h averages 40, not 45 — you spent twice as long at the slow speed.
- Growth rates compound. +50% then −50% is not 0% — it's −25%. Multi-year returns average geometrically, which is why our investment calculator never simply averages annual figures.
From the Blog
// Outliers
A single extreme value can skew the mean dramatically. When in doubt, check the median too — if they differ significantly, your data is skewed.
// IQR
The interquartile range (IQR = Q3−Q1) measures spread for the middle 50% of data. It's more robust than range when outliers exist.
// Sample vs Population
If your numbers are a sample (not the whole group), use sample std deviation (s) — it gives a less biased estimate of the true spread.
// No Mode
If every value appears exactly once, there is no mode. If multiple values tie for most frequent, all are modes (multimodal dataset).