Statistics Calculator
Get the full descriptive statistics for a dataset: mean, median, mode, range, variance and standard deviation.
What this tool does
A statistics calculator calculates the full descriptive statistics set for a dataset: mean, median, mode, range, variance and standard deviation. Paste the numbers - separated by commas, spaces or new lines, sorted or not - and it returns the centre (mean, median, mode), the spread (range, variance, standard deviation) and the quartiles, with the count. Both population and sample standard deviation are shown, because they differ by the square of n ÷ (n − 1) and using the wrong one is the classic statistics error.
Calculates the full descriptive statistics set for a dataset: mean, median, mode, range, variance and standard deviation.
Shows quartiles and the count, so the spread is visible rather than just the centre.
Works from a pasted list of numbers, sorted or unsorted, with duplicate values handled.
Returns population and sample standard deviation side by side.
How to use it
- Paste or type your numbers, separated by commas, spaces or line breaks.
- Negative numbers and decimals are accepted.
- Read the centre: mean, median and mode.
- Read the spread: range, variance and standard deviation (population and sample).
- Check the quartiles for the distribution's shape.
Why use this calculator
Calculating the full descriptive statistics set for a dataset in one pass shows what a single average hides. Two datasets can share a mean and tell completely different stories - one tight around the middle, one spread across the range - and only the standard deviation and quartiles reveal the difference. Whether the data is a class of test scores, a run of measurements or a week of readings, the centre alone is never the whole picture.
Why we built it
We built the statistics calculator to return population and sample standard deviation together, because choosing between them is where careless analysis goes wrong. Population divides by n; sample divides by n − 1, which corrects the bias when your data is a sample of something larger - which it almost always is. The mean-median-mode-calculator covers just the centre, the z-score-calculator standardises a single value, and the percentile-calculator locates one point in the distribution.
For what the sample implies about the whole, the confidence-interval-calculator and the sample-size-calculator take the next step, and the weighted-average-calculator applies importance weights instead.
Who this tool is for
- Students summarising a dataset for coursework or an exam
- Researchers checking a sample before formal analysis
- Anyone comparing spreads rather than just averages
- Quality or operations teams reviewing measured readings
When to use it
- After collecting a sample, before any modelling.
- Comparing two groups' spread as well as their means.
- Checking whether the median suits better than the mean.
- Preparing descriptive statistics for a report.
How it is calculated
Mean = Σx ÷ n. Median = the middle value once sorted, or the average of the two middle values for an even count. Mode = the most frequent value. Range = max − min. Variance = Σ(x − mean)² ÷ n (population) or ÷ (n − 1) (sample). Standard deviation = the square root of the variance. Quartiles split the sorted data into four equal parts.
Worked example: the dataset 4, 8, 6, 5, 3, 8, 9 has n = 7, mean = 43 ÷ 7 = 6.14, median = 6, mode = 8, range = 9 − 3 = 6. The sum of squared deviations is 30.86, so population variance = 30.86 ÷ 7 = 4.41, giving population standard deviation 2.10, and sample standard deviation = √(30.86 ÷ 6) = 2.27.
The mean is pulled by outliers while the median is not. A single extreme value can move the mean substantially and the median not at all - which is why income, house prices and reaction times are usually reported with medians.
Population or sample?
| Your data | Use | Divisor |
|---|---|---|
| Every member of the group | Population σ | n |
| A sample of a larger group | Sample s | n − 1 |
| Small sample under 30 | Sample s | n − 1 (difference is large) |
| Reported in a paper | Sample s, unless stated | State which you used |
The two agree closely for large samples and diverge sharply for small ones - with n = 2 the sample figure is 41% larger. Always label which one you are quoting.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change the dataset on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Dataset | 4, 8, 6, 5, 3, 8, 9 |
| Count | 7 |
With that dataset, the calculator returns:
- Mean: 6.14
- Median: 6
- Mode: 8
- Range: 6
- Population variance: 4.41 · standard deviation: 2.10
- Sample variance: 5.14 · standard deviation: 2.27
- Quartiles: 4, 6, 8
Reading the spread
Standard deviation in the same unit as the data is the quickest read: about 68% of values fall within one standard deviation of the mean, 95% within two, if the distribution is roughly bell-shaped. Skewed or heavy-tailed data breaks that rule, which is why the quartiles are shown too - they describe the distribution without assuming any shape.
| Measure | Tells you | Sensitive to outliers? |
|---|---|---|
| Range | Total width of the data | Very |
| Standard deviation | Typical distance from the mean | Yes |
| Interquartile range | Width of the middle 50% | No |
| Variance | Spread squared - used in further maths | Yes |
What you enter, and what you get back
| Item | Details |
|---|---|
| Dataset | Any list of numbers, any separator, any order. |
| Result | Count, mean, median, mode, range, variance, standard deviation and quartiles. |
| Standard deviation | Both population (÷ n) and sample (÷ n − 1). |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| No mode returned | Every value appears equally often. | That is correct - the data is amodal. |
| Mean far from the median | Skew or an outlier. | Report the median and the quartiles as well. |
| Standard deviation looks too big | Two very different groups mixed together. | Check whether the data combines distinct populations. |
| Numbers ignored | Stray characters or units in the paste. | Clean the list; only numbers, commas and spaces. |
Assumptions and limitations
- Descriptive only - it summarises the data you enter and infers nothing about a wider population.
- Quartiles follow the common interpolation method; other conventions differ by one position.
- Assumes numeric, independent values; repeated measurements of the same subject are not independent.
- For distributions far from bell-shaped, the 68-95 rule does not apply.
Frequently asked questions
How do I calculate mean, median and mode?
Mean is the sum divided by the count. Median is the middle value once sorted, averaging the two middle values for an even count. Mode is the value appearing most often. For 4, 8, 6, 5, 3, 8, 9: mean 6.14, median 6, mode 8.
How do I calculate variance and standard deviation?
Subtract the mean from each value, square the differences, sum them, then divide by n for population variance or n − 1 for sample variance. Standard deviation is the square root of the variance. For the dataset 4, 8, 6, 5, 3, 8, 9 the population variance is 4.41 and the standard deviation 2.10.
What is the difference between population and sample standard deviation?
Population standard deviation divides by n and describes the whole group. Sample standard deviation divides by n − 1, correcting the bias when your data represents a larger population - which is the usual case. The sample figure is always the larger of the two, and the gap is significant for small samples.
How do I find quartiles from a dataset?
Sort the data, find the median (Q2), then find the median of the lower half (Q1) and the upper half (Q3). The interquartile range is Q3 − Q1 and covers the middle 50% of values. Methods differ slightly for small or even-sized datasets; the calculator uses the standard interpolation approach.
How do I enter a dataset into a calculator?
Paste the numbers separated by commas, spaces or line breaks - the calculator accepts all three, in any order, with negatives and decimals. Spreadsheet columns copy in directly. Stray text or units are ignored, but clean the list first so nothing is silently dropped.
What does the range tell me about data?
The range is the largest value minus the smallest, giving the total width the data covers. It is quick but fragile: one outlier can dominate it entirely. Read it with the standard deviation and interquartile range, which describe the typical spread rather than the extremes.