Average Calculator (Mean / Median / Mode)
Paste or type a list of numbers (comma-, space- or newline-separated) and instantly see the mean, median, mode and range — plus sum, min/max, population standard deviation, variance and the sorted list.
Mean
—
sum ÷ count
Median
—
middle value when sorted
Mode
—
most-frequent value
Range
—
max − min
Other statistics
- Count
- —
- Sum
- —
- Min
- —
- Max
- —
- Std. dev. (σ)
- —
- Variance (σ²)
- —
- Sorted ascending
- —
Standard deviation and variance use the population formula (divide by n). For a sample, divide by n − 1 instead.
Formula
Mean = Σxᵢ ÷ n Median = middle value when sorted (mean of the middle pair if n is even) Mode = value(s) with the highest frequency (none if no repeats; multimodal if tied) Range = max − min Variance σ² = Σ(xᵢ − μ)² ÷ n (population formula) Std. dev. σ = √σ²
- · The mean is sensitive to outliers; the median is more robust, which is why incomes, property prices and exam scores are usually reported as medians.
- · Median rule: sort the values, take the middle one if the count is odd, or average the middle pair if the count is even.
- · Mode can be empty (no repeats) or multimodal (several values tied for the highest frequency). The tool lists every tied mode.
- · Standard deviation and variance use the population formula (divide by n). Sample-based work typically uses n − 1 (Bessel correction); the displayed values are easy to convert by hand if needed.
- · Negatives and decimals are accepted. Separate values with commas, spaces, semicolons or newlines. Invalid tokens are flagged but never block the rest of the calculation.
- · This is descriptive statistics only — inferential procedures such as t-tests or confidence intervals are out of scope.
Frequently asked
When should I use mean, median or mode?
Use the mean when the data is roughly symmetric with no extreme outliers — e.g. quiz scores. Use the median when the distribution is skewed or has outliers, like incomes or housing prices: a few extreme values can pull the mean far from the middle of the data. Use the mode mostly for categorical or discrete data — the most popular shoe size, the most common BMI bucket. Mode of continuous measurements usually has little meaning.
What does the tool show when there are no repeated values?
If every value appears exactly once (no frequency ≥ 2), the mode is mathematically undefined. The tool shows "—" in the mode field with a note saying "No repeats — no mode". When two or more values tie for the highest frequency, all of them are listed and the panel is labelled "Multimodal".
Does the standard deviation use n or n − 1?
The tool reports the population standard deviation (divide by n). When you treat your data as a sample meant to infer something about a wider population, the convention is to divide by n − 1 (Bessel's correction, sample SD). The two differ by a single factor: sample_sd = pop_sd × √(n ÷ (n − 1)). For typical high-school datasets of a few dozen points, the gap is usually under 5%.
Can I paste a row of numbers from Excel?
Yes. Copy a row or column from Excel or Google Sheets and paste it in — tabs and spaces are treated as separators. Commas, semicolons and newlines all work too. Invalid tokens (like "N/A" or "two") are flagged in red but never block the rest of the calculation.
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