ƒ MATH · EIGHT CALCULATION MODES

Statistics Calculator

Find count, sum, mean, median, minimum, maximum, variance and standard deviation. Choose sample or population statistics for your data. How to use it ↓

Find count, sum, mean, median, minimum, maximum, variance and standard deviation. Choose sample or population statistics for your data.

Data Variance and standard deviation

Enter up to 1,000 numbers separated by spaces, commas or new lines. Sample statistics need at least two values.

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About this result

Results round to 12 significant digits. Exact arithmetic fractions are available where supported.

Expression reference

sin(30) · asin(0.5)
ln(e) · log(8,2)
root(27,3) · 2^3
5! · nCr(5,2)
sinh(1) · conj(3+4i)
re(3+4i) · arg(3+4i)
1e-5 · 200+10%

Use exp(x) for eˣ and mod(a,b) for the remainder. Roots and logarithms may return complex values.

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How to use the statistics calculator

Enter your numbers separated by spaces, commas or new lines.
Choose Sample when your data represent a sample, or Population when they contain the full group you are describing.
Select Calculate to read the summary statistics.
Check the count and sample/population selection before using the variance or standard deviation.

Formula and method

Mean = Σxᵢ / n; sample variance = Σ(xᵢ − mean)² / (n − 1)

Mean, median and spread

The mean uses every value in the sum divided by the count. The median is the middle sorted value, or the average of the middle pair for an even count. Minimum and maximum give the endpoints of the observed data. An outlier can strongly affect the mean and spread even when the median changes little.

Sample versus population variance

Population variance divides squared deviations by n. Sample variance uses n−1, accounting for a mean estimated from the sample. Standard deviation is the square root of variance and has the same units as the original observations; variance has squared units.

ONE TOOL, DIFFERENT TASKS

Choose the mode for your calculation

Scientific Calculator

Powers, roots, logarithms, trigonometry, factorials, combinations and permutations. Decimal and exact arithmetic fraction displays, Ans and memory.

Complex Number Calculator

Calculate with i. Read the rectangular result, magnitude, argument and conjugate. Angle units apply to the argument and trigonometric functions.

Matrix Calculator

Add, subtract and multiply matrices up to 4 × 4. Find a determinant, inverse or transpose. Matrix B is needed only for binary operations.

Numerical Calculus Calculator

Approximate a definite integral or a derivative at a real point. This is numerical calculus; it does not produce symbolic antiderivatives.

Equation Solver

Solve a quadratic, including complex roots, or a system of two or three simultaneous linear equations. Degenerate quadratic inputs are handled as linear equations.

Statistics Calculator

Find count, sum, mean, median, range endpoints, variance and standard deviation for up to 1,000 values. Choose sample or population statistics.

Base-N Calculator

Convert signed integers of up to 128 bits between binary, octal, decimal and hexadecimal. Bitwise operations use unsigned 32-bit operands.

Function Table Calculator

Evaluate a real-valued function over a range of x values. Choose start, end and step; each table supports up to 201 rows.

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Statistics Calculator worked examples

Find sample standard deviation

10, 20, 30

Mean=20; sample standard deviation=10

Squared deviations sum to 100+0+100=200. Dividing by n−1=2 gives variance 100; its square root is 10.

Compare population variance

10, 20, 30; Population

Variance≈66.6667; standard deviation≈8.16497

With the same data, divide the squared deviations of 200 by n=3 instead of n−1.

READ THE RESULT WITH CONTEXT

Accuracy, notation and limits

The input accepts at most 1,000 finite numeric values. Sample variance needs at least two observations. Population variance for a single observation is zero. Do not include currency signs or thousands separators inside individual values.

Each listed value counts as one equally weighted observation. This page does not calculate weighted statistics, regression, confidence intervals or inferential tests. Results are rounded for display; numerical precision can be limited for very large values.

Read our calculation methodology ↗

COMMON QUESTIONS

Statistics Calculator FAQs

Should I choose sample or population?

Choose Population if the values describe the entire group you mean to analyze. Choose Sample if the values are a sample and you need the n−1 variance estimate.

Are commas allowed in a number such as 1,000?

Commas separate observations here. Enter one thousand as 1000; entering 1,000 would be interpreted as two values, 1 and 000.

Does this calculate mode or weighted mean?

This page reports descriptive statistics including mean, median and standard deviation. Use the linked Mean, Median & Mode or Weighted Average tools for those additional tasks.

Calculation library: math.js. This page is an independent CalcPebble tool.