Paste or type a list of numbers and get every basic statistical measure at once - count, sum, mean, median, mode, min, max, range, variance and standard deviation (population and sample), and the quartiles Q1, Q3 with IQR. Useful for class projects, exam prep, lab data analysis and quick checks on small datasets.
Count
10
Sum
289
Mean (average)
28.9
Median
28.5
Mode
30
Range
38
Min
12
Max
50
Std Deviation (population)
10.387011
σ - divide by N
Std Deviation (sample)
10.948871
s - divide by N − 1
Variance (population)
107.89
Variance (sample)
119.877778
Q1 (25th percentile)
22.75
Q3 (75th percentile)
33.75
IQR (Q3 − Q1)
11
Middle 50% spread
Parte del contenido aún se muestra en inglés.
Descriptive statistics summarise a dataset in just a few numbers - central tendency (mean, median, mode), spread (range, variance, standard deviation, IQR), and shape (quartiles). These measures are the foundation of every statistical analysis, from Class 11 NCERT statistics chapters through to advanced data science. Understanding them - and computing them quickly - is essential for academic work, business reporting, scientific research, and any quantitative decision-making.
This calculator handles the full set of standard descriptive statistics simultaneously, so you get the complete picture with one paste. Just enter or paste your data (from Excel, Google Sheets, or any list) and see all measures update live. The Population vs Sample toggle is critical: sample statistics use Bessel's correction (dividing by N−1 instead of N) to give unbiased estimates of population parameters from a random subset. This calculator implements both correctly.
Paste your data into the textbox - separated by spaces, commas, semicolons or new lines.
Non-numeric entries are silently dropped (so pasting from a spreadsheet column works).
All summary statistics update as you type or paste.
Toggle between Population and Sample variance/standard deviation if needed.
Use the Clear button to start over.
Mean adds all values and divides by count. Median is the middle value (or average of the two middle values for even count). Mode is the most-frequent value(s) - there may be more than one. Variance averages the squared deviations from the mean; standard deviation is the square root of variance. Population variance divides by N; sample variance divides by N − 1 (Bessel's correction) to give an unbiased estimate when the data is a sample of a larger population. Quartiles use the linear-interpolation method (Excel / R-7), so they match what most spreadsheets show.
Variance = Σ(xᵢ − x̄)² / N Sample variance uses (N − 1) instead
Central tendency measures three different things. Mean (arithmetic average) is sensitive to all values, so a single outlier can shift it dramatically. Median (middle value when sorted) is robust to outliers - half the data lies above and half below. Mode is the most-frequent value, useful for categorical-like data or detecting bimodal distributions. For symmetric, normally-distributed data, all three coincide; for skewed data they diverge meaningfully. Indian household income, for example, is right-skewed: mean is far higher than median because a few very high earners pull the mean up.
Dispersion measures the spread. Range (max − min) is simple but sensitive to outliers. Variance averages the squared deviations from the mean - squaring makes positive and negative deviations both contribute and amplifies the influence of large deviations. Standard deviation is the square root of variance, returning to the same units as the original data, making it directly interpretable. IQR (interquartile range, Q3 − Q1) captures the spread of the middle 50%, robust to outliers.
Population vs sample distinction: when your data covers every member of the group of interest (e.g., all 30 students in your class), use population stats - divide by N. When the data is a random sample from a larger population you want to estimate (e.g., 500 voters polled to estimate election results), use sample stats - divide by N−1. The N−1 correction (Bessel's correction) accounts for the loss of one degree of freedom when the sample mean is used as the estimate of the population mean. Wrong choice gives biased standard deviation estimates.
N=10. Mean: 80. Median: 79 (avg of 78 and 80). Mode: no repeat - amodal. Range: 30. Sample variance: 102.67. Sample SD: 10.13. Q1: 71.5, Q3: 87.25. IQR: 15.75. Distribution roughly normal - mean ≈ median.
Mean: 16.5 (skewed by outlier). Median: 8 (much more representative). Mode: 7 and 8 (bimodal). Range: 75. Population SD: 21.9 (huge, due to ₹80L outlier). When data is heavily skewed, median is the better central tendency measure than mean.
Use population when you have data for every member of the group (e.g. all students in a class). Use sample when your data is a random subset of a larger group you want to estimate (e.g. survey data). Sample SD divides by N − 1 to compensate for the bias that comes with estimating from a sample.
Mean is the arithmetic average. Median is the middle value when sorted. Mode is the most-frequent value (or values, if there's a tie). For symmetric distributions, all three are similar; for skewed data they differ - for example, income is right-skewed so the mean is much higher than the median.
Yes. Mean, sum, count, mode, variance and SD don't depend on order. Median and quartiles sort internally before computing.
Q3 − Q1 - the spread of the middle 50% of the data. It's a robust measure of dispersion, less sensitive to outliers than range or standard deviation. Used to detect outliers (anything beyond Q1 − 1.5·IQR or Q3 + 1.5·IQR).
Max − Min. Simple but very sensitive to outliers, so it's mainly useful as a sanity check.
If every value appears exactly once, the data is amodal. The calculator shows "No mode" in that case rather than listing every value.
There's no hard limit - calculations run in milliseconds even for thousands of values. Browser performance is the only practical constraint.
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Statistics Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.
