Statistics Calculator
Enter a list of numbers and instantly get mean, median, mode, standard deviation, variance, quartiles, and more. All calculations run in your browser — nothing is sent to a server.
All calculations happen in your browser. No data is stored.
Enter Your Numbers
Enter numbers separated by commas or new lines
Results
| Statistic | Value |
|---|---|
| Count | — |
| Sum | — |
| Mean (average) | — |
| Median | — |
| Mode | — |
| Range | — |
| Minimum | — |
| Maximum | — |
| Population Std Dev (σ) | — |
| Sample Std Dev (s) | — |
| Population Variance (σ²) | — |
| Sample Variance (s²) | — |
| First Quartile (Q1) | — |
| Third Quartile (Q3) | — |
| Interquartile Range (IQR) | — |
Understanding Your Statistics
Mean vs Median
The mean (arithmetic average) sums all values and divides by the count. It is easy to calculate but sensitive to outliers — one extreme value can pull it far from the center.
The median is the middle value when data is sorted. It is resistant to outliers and often better represents a "typical" value in skewed distributions, such as income or home prices.
Standard Deviation Explained
Standard deviation (σ or s) measures how spread out values are around the mean. A small standard deviation means values cluster tightly; a large one means they scatter widely.
Use population std dev (σ) when your numbers are the entire group. Use sample std dev (s) when your numbers are a subset of a larger population — it applies a correction factor (divides by n−1) to avoid underestimating variability.
Quartiles and IQR
Quartiles split sorted data into four equal parts. Q1 is the 25th percentile (25% of data falls below it) and Q3 is the 75th percentile.
The interquartile range (IQR = Q3 − Q1) spans the middle 50% of your data. It is a robust measure of spread unaffected by extreme values. Values more than 1.5 × IQR outside Q1 or Q3 are commonly flagged as outliers.
When Statistics Matter
- Education: Analyze test scores, grade distributions, and class performance.
- Science & research: Summarize experimental data and report variation.
- Business: Understand sales distributions, customer metrics, and response times.
- Finance: Measure portfolio return volatility and risk.
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What is the difference between mean and median?
The mean is the sum of all values divided by the count. The median is the middle value of a sorted data set. The mean is affected by outliers; the median is not. For example, in the data set 1, 2, 3, 4, 100 the mean is 22 but the median is 3. For skewed distributions, the median is usually the more representative measure of center.
What is standard deviation and what does it tell me?
Standard deviation quantifies how much individual values in a data set typically differ from the mean. If the standard deviation is low, most values are clustered close to the mean. If it is high, values are spread out. In a normal distribution, roughly 68% of values fall within one standard deviation of the mean, and about 95% fall within two.
When should I use population vs sample standard deviation?
Use population standard deviation (σ) when your data set contains every member of the group you are studying. Use sample standard deviation (s) when your data is a random sample taken from a larger population and you want to estimate the true variability of that population. The sample formula uses n−1 in the denominator (Bessel's correction) to compensate for the fact that a sample tends to underestimate the spread of the full population.
What is the interquartile range (IQR) used for?
The IQR is the range of the middle 50% of a data set (Q3 minus Q1). It is used as a robust measure of statistical spread that is not influenced by extreme values or outliers. It is also the foundation of the standard box-plot outlier rule: any value more than 1.5 × IQR below Q1 or above Q3 is considered a potential outlier.
What does it mean when mode is "None"?
Mode is the value that appears most often in a data set. When every value appears exactly once (no repeats), there is no mode — this calculator displays "None". A data set can also be bimodal (two modes) or multimodal (more than two modes), in which case all tied values are listed, separated by commas.