Financial calculator category
Statistics & Probability calculators
Statistics & Probability calculators: Calculate averages, spread, combinations, probability and confidence intervals. The category holds 13 tools, including the Mean & Median Calculator, the Standard Deviation Calculator and the Range & Midrange Calculator.
Mean & Median, Standard Deviation and Range & Midrange summarize a data set. Z-Score places one value relative to the group, and Normal Distribution Probability and P-Value from Z-Score turn it into a probability. Confidence Interval and Sample Size support surveys and estimates. For chance problems, use Simple Probability, Binomial Probability, Permutation & Combination, Bayes' Theorem and Expected Value. Start with the mean and standard deviation, then the test or interval you need. Sample size matters.
Among the tools here are Mean & Median Calculator, Standard Deviation Calculator, Range & Midrange Calculator, Permutation & Combination Calculator, Simple Probability Calculator, Z-Score Calculator, Confidence Interval Calculator, Sample Size Calculator, and 5 more that follow the same pattern of formula, worked example, limits and sources.
Pick one below. Open it.
Mean & Median Calculator
Calculate the mean and median of six values.
Open calculator →02Standard Deviation Calculator
Calculate population and sample standard deviation for six values.
Open calculator →03Range & Midrange Calculator
Calculate the range and midrange of six values.
Open calculator →04Permutation & Combination Calculator
Calculate permutations and combinations for choosing r items from n.
Open calculator →05Simple Probability Calculator
Calculate the probability and odds of a simple event.
Open calculator →06Z-Score Calculator
Calculate a z-score and its approximate percentile under a normal distribution.
Open calculator →07Confidence Interval Calculator
Calculate a confidence interval around a sample mean.
Open calculator →08Sample Size Calculator
Calculate the sample size needed for a target margin of error and confidence level.
Open calculator →09Binomial Probability Calculator
Calculate the chance of exactly k successes, and of k or fewer, in n independent trials.
Open calculator →10Normal Distribution Probability Calculator
Calculate the probability that a normally distributed value falls between two limits.
Open calculator →11P-Value from Z-Score Calculator
Calculate the p-value for a z-score in a left-tailed, right-tailed or two-tailed test.
Open calculator →12Expected Value Calculator
Calculate the expected value of a bet or decision from its chance of winning, the amount won and the amount lost.
Open calculator →13Bayes' Theorem Calculator
Calculate the chance of a condition after a positive or a negative test from prevalence, sensitivity and false positive rate.
Open calculator →Go deeper
Statistics & Probability guides
Every tool, one table
Statistics & Probability calculators at a glance
Each row shows the headline figure that calculator returns at its own worked-example inputs.
| Calculator | What it answers | Headline output | Worked example |
|---|---|---|---|
| Mean & Median Calculator | Median resists outliers better than mean; a large gap between them signals skew. | Mean | 16 |
| Standard Deviation Calculator | Use sample deviation for a subset of a larger population, population deviation for the whole thing. | Population standard deviation | 4.5 |
| Range & Midrange Calculator | Range is sensitive to a single extreme value in a way that mean is not. | Range | 13 |
| Permutation & Combination Calculator | Use permutations when order matters, combinations when it doesn't. | Permutations (order matters) | 720 |
| Simple Probability Calculator | Probability assumes every outcome is equally likely. | Probability | 7.7% |
| Z-Score Calculator | The percentile approximation assumes a normal distribution, which not every dataset has. | Z-score | 1.3 |
| Confidence Interval Calculator | A 95% interval means 95% of such intervals would contain the true mean, not a 95% chance this one does. | Lower bound | 94.6 |
| Sample Size Calculator | Smaller margins of error require disproportionately larger samples. | Required sample size | 385 |
| Binomial Probability Calculator | Check the odds of a run of successes before you treat a streak as skill or as bad luck. | Exactly k successes | 11.7% |
| Normal Distribution Probability Calculator | Turn a mean and a standard deviation into the share of results that land inside a range you care about. | Probability between a and b | 68.3% |
| P-Value from Z-Score Calculator | Turn a test statistic into the probability of a result at least as extreme under the null hypothesis. | p-value | 0.05 |
| Expected Value Calculator | Find the average result of a repeated gamble before you take it. | Expected value per attempt | $40 |
| Bayes' Theorem Calculator | See why a positive result on a good test can still mean a low chance of the condition when it is rare. | Chance of the condition after a positive test | 15.4% |
Where people go wrong with statistics & probability numbers
Using the mean when the data is skewed hides the typical value, and the median is often better. Sample and population standard deviation use different divisors, so pick the right one. A p-value is not the probability that a result is true, and a confidence interval is not the chance that the true value lies inside a specific computed range. Combinations count without order and permutations count with it. Look at the data first. Then compute.
Background reading
Statistics & Probability guides
- A/B tests, p-values and Bayes' theoremLearn what a p-value does and does not say, how to run a fair test, and why a positive result from a good test can still be wrong.
Definitions
Statistics & Probability terms
- Combination : glossary term
- A selection of items where order does not matter. Choosing 3 people for a committee from a group is a combination problem.
- Confidence interval : glossary term
- A range built from sample data. It is likely to contain the true population value at a stated confidence level, commonly 95%.
- Margin of error : glossary term
- The plus-or-minus range added to a sample estimate to build a confidence interval. Sample size, variability and the chosen confidence level drive it.
- Permutation : glossary term
- An arrangement of items where order matters. Picking a first, second and third place from a group is a permutation problem.
- Standard deviation : glossary term
- A measure of how spread out a set of values is around its mean. A small standard deviation means values cluster tightly; a large one means they scatter widely.
- Z-score : glossary term
- How many standard deviations a value sits from the mean of its distribution. A z-score of 2 means the value is two standard deviations above average.
Keep exploring
Related calculator categories
Next to the statistics & probability tools, these categories answer the questions that usually come up alongside them.
Common statistics & probability questions
Why use median instead of mean?
Mean is pulled toward extreme values. Median is not. A neighborhood where one mansion sits among modest homes has a mean price far above what a typical home costs, while the median reflects the typical home much better. Large gaps between mean and median signal a skewed distribution.
What's the difference between population and sample standard deviation?
Population standard deviation divides by n and is used when your data IS the entire group you care about. Sample standard deviation divides by (n−1) and is used when your data is a subset meant to estimate a larger population: the smaller divisor corrects for the fact that a sample tends to understate true variability.
What does a 95% confidence interval actually mean?
It means that if you repeated the sampling process many times and built an interval the same way each time, about 95% of those intervals would contain the true population value. It does NOT mean there's a 95% probability the true value falls in this one specific interval: a common and understandable misreading.
Why do smaller margins of error need disproportionately larger samples?
Required sample size grows with the square of how small you want the margin of error to be. Cutting the margin of error in half roughly quadruples the sample size needed, which is why polls rarely promise a margin under 2-3% even with very large samples.
When should I use permutations instead of combinations?
Use permutations when the order of selection matters: first, second and third place in a race are different outcomes. Use combinations when only the group matters, not the order: three people chosen for a committee are the same group regardless of the order they were picked.
What is a normal distribution, and when does it apply?
A bell-shaped curve centered on the mean, with about 68 percent of values within one standard deviation and 95 percent within two. Heights and measurement errors are roughly normal. Incomes and waiting times usually are not.
What are independent trials?
Trials are independent when one outcome does not change the chance of the next. Coin flips are. Drawing cards without putting them back is not. The binomial model needs independence and a fixed chance of success.
Does a streak mean a coin is due to change?
No. Each independent flip has the same chance whatever came before. A long streak is unlikely, but after one the next flip is still even. Believing otherwise is called the gambler's fallacy.
What is the difference between exactly k and k or fewer?
Exactly k is the chance of one specific count. K or fewer adds up every count from zero to k. Ask which one your question needs, because the second is always the larger number.
Why can a positive test on a good test still be unlikely to be right?
When the condition is rare, most positives come from the large group without it. Ninety percent sensitivity and a 5 percent false positive rate can still leave a positive result at about a 15 percent chance of the condition if only 1 percent of people have it.
What does a p-value of 0.05 mean?
It is the chance of seeing a result at least this extreme if there were no real effect. It is not the chance that the effect is real, and a result just under 0.05 is weak evidence on its own.
People also ask
Statistics & Probability calculator questions
What is the difference between mean and median?
The mean is the average, while the median is the middle value, and the median is less affected by extreme values.
What does a z-score tell me?
How many standard deviations a value is above or below the mean, which lets you compare values from different distributions.
When should I use a permutation instead of a combination?
Use a permutation when order matters, such as a race finish, and a combination when it does not, such as picking a committee.