9 free statistics calculators for students, researchers, and data analysts.
Most statistics questions fall into one of three groups, and which calculator you need depends on which group you are in.
| You want to | Use | Because |
|---|---|---|
| Summarise a data set | Statistics Calculator or Mean, Median, Mode & Range | Gives centre and spread in one pass |
| Measure how spread out the data is | Standard Deviation | The average distance of values from the mean |
| Compare a value against a distribution | Z-Score Calculator | Expresses a value as standard deviations from the mean |
| Estimate a population from a sample | Confidence Interval | Gives a range rather than a single misleading number |
| Plan a survey or study | Sample Size Calculator | Works out how many responses you actually need |
| Count arrangements or selections | Permutations & Combinations | Order matters for one, not the other |
| Work out a likelihood | Probability Calculator | Single and combined event probability |
| Find the pattern in a sequence | Number Sequence | Arithmetic and geometric progressions |
All three describe the centre of a data set, and they can disagree sharply. Choosing the wrong one is how statistics gets used to mislead — often without anyone intending to.
| Measure | What it is | Best for |
|---|---|---|
| Mean | Add everything, divide by the count | Symmetric data with no extreme values |
| Median | The middle value when sorted | Skewed data — incomes, house prices, waiting times |
| Mode | The most frequent value | Categories and repeated discrete values |
Australian house prices are the standard illustration. A handful of very expensive sales pull the mean upward, while the median sits where the middle sale actually happened. This is why property reporting and the ABS quote median prices — the mean would describe a market almost nobody is buying in. The same logic applies to salaries, and to any data with a long tail.
Standard deviation and variance have two versions, and picking the wrong one is the single most common mistake in introductory statistics.
Population (σ) → divide by N
Sample (s) → divide by n − 1
The n − 1 is called Bessel's correction. A sample tends to underestimate the true spread of the population it came from, because a sample is unlikely to capture the most extreme values. Dividing by a slightly smaller number nudges the estimate upward to compensate.
The practical rule. If your numbers are the entire group you care about — every student in one class, every transaction last month — use the population formula. If they are a subset you are using to say something about a larger group, use the sample formula. When in doubt in a course context, it is usually the sample version, and the calculators here show both so you can see how far apart they land.
These two are the same idea approached from opposite ends. A confidence interval tells you how precise an existing result is; a sample size calculation tells you how many responses you need for a target precision.
Roughly: margin of error ∝ 1 ÷ √n
That square root is the reason survey costs rise so steeply. Halving your margin of error requires roughly four times the sample, not twice — which is why national polls tend to settle around 1,000 to 1,500 respondents. Beyond that the precision gained stops justifying the cost.
A 95% confidence interval does not mean 95% probability the true value is inside it. It means that if you repeated the whole study many times, about 95% of the intervals produced would contain the true value. The distinction sounds pedantic and is the single most misreported idea in statistics — including in news coverage of polling.
The difference is one question: does the order matter?
| Order matters? | Example | |
|---|---|---|
| Permutation | Yes | Finishing positions in a race — 1st, 2nd, 3rd are different outcomes |
| Combination | No | Lottery numbers — drawing 7, 12, 30 is the same as 30, 12, 7 |
There are always more permutations than combinations of the same size, because every combination can be arranged in multiple orders. Choosing 3 people from 10 gives 120 combinations but 720 permutations — the same selections, counted six ways each.
1. Using the mean on skewed data. Incomes, prices and waiting times almost always want the median.
2. Mixing up sample and population formulas. Divide by n − 1 for a sample, N for a population.
3. Reading a 95% confidence interval as a 95% probability. It describes the method's long-run behaviour, not this one interval.
4. Assuming a bigger sample fixes a biased one. If the sample is not representative, more of it just makes the wrong answer more precise.
5. Treating correlation as cause. Two things moving together does not establish that one drives the other.
6. Reporting more decimal places than the data supports. A mean of 4.2857143 from seven whole numbers implies precision that is not there.
The calculators show their working because the working is usually the point. A student checking homework needs to see where a number came from, not just that it matches. A researcher planning a study needs the sample size reasoning, not only the figure. And anyone reading a survey result benefits from understanding what a margin of error actually claims.
If you are working through a course, start with the Statistics Calculator — it produces every descriptive measure at once, which makes it easy to see how the measures relate on the same data. For assignment marks and weighted averages, the grade calculator and GPA calculator handle the arithmetic those need.
Australian Bureau of Statistics — Statistical publications · ABS — Statistical Language guide · OpenStax — Introductory Statistics (open textbook)