Statistics Calculators — Mean, Median, Mode, Standard Deviation & More
Free statistics calculators with step-by-step solutions. Enter your data set and instantly calculate mean, median, mode, standard deviation, variance, range, percentiles, and five number summary.
Choose a Calculator
Mean / Average Calculator
Calculate arithmetic, geometric, and harmonic mean. Enter any list of numbers.
Median Calculator
Find the median, Q1, Q3, and IQR of your data set.
Mode Calculator
Find the mode and frequency distribution of your data.
Standard Deviation Calculator
Population (σ) and sample (s) standard deviation with step-by-step work.
Variance Calculator
Calculate population and sample variance with full breakdown.
Range Calculator
Find the range, min, max, and sorted data of any number set.
Percentile Calculator
Calculate any percentile (P25, P50, P75, P90) and percentile rank.
Five Number Summary
Min, Q1, Median, Q3, Max — with visual box plot.
Measures of Central Tendency vs Spread
| Measure | What It Tells You | Best For | Outlier Sensitive? |
|---|---|---|---|
| Mean | Average value | Symmetric data | Yes |
| Median | Middle value | Skewed data | No |
| Mode | Most frequent value | Categorical data | No |
| Range | Total spread | Quick overview | Yes |
| Std Dev | Average distance from mean | Normal distribution | Yes |
| IQR | Middle 50% spread | Skewed data | No |
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the arithmetic average (sum ÷ count). Median is the middle value when data is sorted. Mode is the most frequent value. Use median for skewed data, mean for symmetric data, and mode for categorical data.
Should I use population or sample standard deviation?
Use population (σ) when you have data for the entire population. Use sample (s) when working with a subset — this is more common. The sample formula uses Bessel’s correction (n−1) to reduce bias.
What is a five number summary?
The five number summary: Min, Q1, Median, Q3, Max. It provides a complete overview of data distribution and is the basis for box plots.
How do I calculate standard deviation?
1) Calculate the mean. 2) Subtract the mean from each value. 3) Square each deviation. 4) Sum the squared deviations. 5) Divide by n (population) or n−1 (sample). 6) Take the square root.
