Get the full set of descriptive statistics — mean, median, mode, variance, standard deviation, quartiles, IQR, range and skewness — from any dataset.
Results update live as you type.
Mean (average)
Median
8
middle value
Mode
None
most frequent
Std Deviation
4.47
s · sample
Range
14
max − min
Variance
20
s² · sample
Q1 · Q3
4 · 12
25th · 75th pct
IQR
8
Q3 − Q1
Skewness
0
symmetric
| Statistic | What it tells you | Robust to outliers? |
|---|---|---|
| Mean | Arithmetic centre of the data | No |
| Median | Middle value when sorted | Yes |
| Mode | Most frequently occurring value(s) | Yes |
| Std deviation | Typical spread around the mean | No |
| IQR | Spread of the middle 50% of data | Yes |
| Range | Spread between min and max | No |
The Method
Descriptive statistics summarise a dataset with a handful of meaningful numbers. The mean sums every value and divides by n. The median is the middle value once the data is sorted. Variance measures average squared distance from the mean — the standard deviation is its square root, in the same units as the original data. Quartiles split the sorted data into four equal parts. Whether you divide by n or n − 1 depends on whether your data is a full population or a sample.
Working for your dataset
About This Tool
A statistics calculator takes a list of numbers and returns the full set of descriptive statistics in one shot — the measures statisticians, researchers, students and analysts use to summarise data. Enter any dataset and this tool reports the count, sum, mean, median, mode, minimum, maximum, range, variance, standard deviation, quartiles, interquartile range (IQR) and skewness.
The first decision when describing data is central tendency — what is a typical value? The mean uses every value but is pulled by outliers; the median is the middle value and is robust to extremes; the mode is the most frequent value (or values). For a symmetric distribution all three coincide; in skewed data they diverge in predictable ways.
The next question is spread — how dispersed are the values? Range is simply max − min. Variance and standard deviation measure average distance from the mean (in squared and original units, respectively). The IQR, the spread of the middle 50%, gives a robust alternative used in box plots and outlier detection.
Use this free statistics calculator for homework, lab reports, A/B test analysis, quality-control inspection, sports analytics, or anywhere you need to summarise a column of numbers. All computation runs in your browser — no sign-up, no tracking, no data leaves your device.
All Central Tendencies
Mean, median and mode side-by-side so you can pick the right one.
Spread Measures
Variance, standard deviation, range and IQR — both robust and classical.
Skewness
Quantifies asymmetry of the distribution (Pearson moment skewness).
Sample vs Population
Toggle between n and n − 1 denominators for variance and std dev.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Frequency Chart
Built-in histogram of the distribution to spot patterns visually.
Paste your numbers, pick sample or population, read the full summary.
Type or paste any list of numbers — separated by commas, spaces or new lines. Decimals and negatives are accepted, and non-numeric tokens are ignored.
If your data is a sample from a larger group, use the default (n − 1 denominator). If you have the entire population, switch to "Population" (n denominator).
The summary card headlines the mean with median and mode immediately beside it. Compare the three — if mean ≠ median your data is likely skewed.
Check std deviation for typical distance from the mean, and IQR for the spread of the middle 50%. Large gaps between range and IQR signal extreme values.
Positive skew = long right tail; negative skew = long left tail. |skew| < 0.5 is roughly symmetric; > 1 is highly skewed.
The bar chart shows how often each value (or bin) occurs — useful for spotting bimodal data, gaps and outliers at a glance.
Everything you need to know about descriptive statistics and how to read this calculator's output.
A population is the entire group you care about; a sample is a subset drawn from it. Population variance divides by N, while sample variance divides by n − 1 (Bessel's correction) to give an unbiased estimate of the true population variance. The same correction applies to standard deviation. In most real-world analysis you have a sample, so the default here is sample statistics.
The mean is best for roughly symmetric data without extreme outliers — it uses every value, which is statistically efficient. The median is the better choice for skewed data (income, house prices, response times) or any dataset with outliers, because it isn't pulled by extreme values. As a rule of thumb, if mean and median differ noticeably, report the median.
The IQR is the spread of the middle 50% of the data: Q3 − Q1. It is robust to outliers and is the basis of box plots. A common rule flags any value beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR as a potential outlier (the "Tukey fence").
Skewness measures asymmetry. Positive skew means a long tail on the right (mean > median) — common in income data. Negative skew means a long tail on the left (mean < median). Zero indicates symmetric data. As a rough guide: |skew| < 0.5 is approximately symmetric; 0.5–1 is moderately skewed; > 1 is highly skewed.
If every value occurs exactly the same number of times, there is no single mode and we report "None". A dataset can be unimodal (one mode), bimodal (two), or multimodal. Modes are most informative on discrete or categorical data — on continuous data, modes from raw values are often meaningless and you should use a histogram or kernel density estimate instead.
Paste values separated by commas, spaces or new lines — the parser handles any combination. Decimals and negative numbers are accepted. Non-numeric tokens are silently ignored, so you can paste straight from a spreadsheet column.
We use the linear interpolation method (Type 7 in R, the most common default): sort the data, find the position (n+1)·q, then linearly interpolate between adjacent values. Other quartile methods exist (eight in total in R) and can produce slightly different results on small datasets — but they all converge as n grows.
Both measure spread. Variance is the average squared distance from the mean — in squared units, so harder to interpret. Standard deviation is the square root of variance, back in the original units. SD is what you typically report; variance is what you use in further calculations (ANOVA, regression).
The calculator runs in your browser and easily handles tens of thousands of values with no perceptible delay. Beyond that — millions of rows — you'll want a dedicated data tool (Excel, Python pandas, R) for both performance and richer statistical features (confidence intervals, hypothesis tests, regression).
Yes. The calculator accepts any real number — negative, decimal, or scientific notation (e.g. 1.2e-3). Calculations use IEEE 754 double-precision floating point, accurate to about 15–17 significant digits.
No. Every calculation runs locally in your browser using JavaScript. Your dataset never leaves your device — no upload, no tracking, no analytics on the values themselves. Safe for sensitive or confidential numbers.
A negatively skewed distribution has a long tail on the left: most values cluster at the high end with a few unusually low ones. Test scores where almost everyone scored well except a handful are classically negatively skewed. The mean will sit to the left of the median.