Statistics & Probability
Combinations & Permutations
nCr = n! / (r!(n−r)!) · nPr = n! / (n−r)!
Selection and arrangement counts for combinatorics problems.
Calculate →Confidence Interval
CI = x̄ ± z · (σ / √n)
Margin of error for a population mean from sample size, mean, and standard deviation.
Calculate →Mean, Median, Mode & Range
μ · M · mode · range
Central tendency and spread summary for any dataset.
Calculate →Probability
P(A) = favorable / total
Basic probability of independent and dependent events from outcome counts.
Calculate →Sample Size
n = (z · σ / E)²
Survey sample size for a target margin of error and confidence level (Cochran formula).
Calculate →Standard Deviation
σ = √(Σ(x − μ)² / N)
Population and sample standard deviation from a dataset.
Calculate →Statistics
μ · σ · σ² · range · IQR
Full summary statistics — mean, variance, standard deviation, range, quartiles — for a dataset.
Calculate →Variance
σ² = Σ(x − μ)² / N
Population and sample variance from a dataset.
Calculate →Z Score
z = (x − μ) / σ
Standardized score and cumulative probability under the standard normal curve.
Calculate →Statistics and probability calculators for descriptive statistics (mean, median, mode, range), dispersion (variance, standard deviation), inferential statistics (confidence interval, sample size), and probability theory (combinations, permutations, basic probability).
Each calculator accepts a comma-separated list or per-element input and shows the formula substitution alongside the result.
When to use these calculators
Use the descriptive stats calcs (mean, median, mode, range, standard deviation, variance) for any dataset summary. Use the z-score calculator to standardize a value against a known mean and standard deviation. Use Confidence Interval and Sample Size for survey design and polling work. Use Combinations & Permutations for combinatorics problems.
Formulas follow standard textbook conventions; sample vs population standard deviation is selectable where applicable.
Frequently Asked Questions
- What is a z-score?
- A z-score is the number of standard deviations a value lies above or below the mean: z = (x − μ) / σ. The Z Score calculator converts between raw values, z-scores, and cumulative probabilities under the standard normal curve.
- Sample or population standard deviation — which do I use?
- Population standard deviation (divide by N) when the dataset is the entire population. Sample standard deviation (divide by N − 1, Bessel's correction) when the dataset is a sample drawn from a larger population. The Standard Deviation calculator supports both.
- How do I choose a sample size for a survey?
- Sample size depends on the population size, desired confidence level (95% is standard), and acceptable margin of error. The Sample Size calculator implements the Cochran formula for proportion estimation; enter your confidence level, margin, and expected proportion.