Statistics calculators
Standard deviation, probability, regression, and analysis tools
4 calculators · 3 guides
Statistics tools here handle the everyday calculations behind reading a data set or designing a survey: central tendency, spread, how unusual a value is, basic probability, and how many responses you need for a given margin of error.
The distinction that trips people up most is population versus sample. Dividing by the number of values gives the population figure; dividing by one less gives the sample estimate, which is larger and is the correct choice when your data are a sample of something bigger. These pages report both and say which is which.
Start with these in Statistics
Standard Deviation CalculatorCalculate sample and population standard deviation, variance, mean and standard error for any list of numbers, with the working shown.StatisticsMean, Median, Mode CalculatorPaste a data set and get the mean, median, mode, range, quartiles and interquartile range, with the sorted list laid out so you can see the middle.Math & ConversionZ-Score CalculatorConvert a value into a z-score, percentile and p-value against the standard normal distribution, with a z-table extract for checking.StatisticsProbability CalculatorTurn favourable and total outcomes into a probability, a percentage, odds and decimal odds, then extend it across repeated independent trials.StatisticsSample Size CalculatorWork out how many responses a survey needs for a given confidence level and margin of error, with the finite population correction applied.Statistics
Every Statistics calculator
4 calculators
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- Sample Size CalculatorWork out how many responses a survey needs for a given confidence level and margin of error, with the finite population correction applied.
- Standard Deviation CalculatorCalculate sample and population standard deviation, variance, mean and standard error for any list of numbers, with the working shown.
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Guides for Statistics
- 8 min readStatistics Fundamentals: Understanding DataLearn the core concepts of statistics including mean, standard deviation, distributions, and when to use each measure.
- 8 min readProbability and Odds: Reading Chance Without Fooling YourselfIndependent versus dependent events, why the gambler's fallacy is so persuasive, and how base rates make accurate tests misleading.
- 8 min readReading Data Without Being Fooled: Averages, Spread and SamplingWhen the mean misleads, what standard deviation actually tells you, and how to judge a survey or a headline statistic.
Questions about statistics calculators
- Population or sample standard deviation?
- Use the population figure only when your numbers are the entire group you care about. Every student in one class, every machine on one line. Use the sample figure whenever the data represent a wider group, which is almost always. The sample version divides by one fewer than the count, correcting the tendency of a sample to understate the true spread.
- What sample size do I need for a survey?
- For a large population, roughly 385 responses give a five per cent margin of error at ninety-five per cent confidence, and about 1,067 give three per cent. Precision improves with the square root of the sample, so halving the margin of error costs four times the responses. Non-response bias usually matters more than the last percentage point of margin.
- What does a z-score actually tell me?
- How many standard deviations a value sits from the mean, which converts any measurement onto a common scale. A z-score of 2 sits above roughly 97.7 per cent of a normal distribution. The caveat is the word normal. For skewed data such as incomes or house prices, percentile interpretations from z-scores are misleading.