Basic statistics

Calculators

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About this tool

Compute descriptive statistics from a bounded list of decimal values. Choose population or sample variance and an explicit missing-value policy.

Common uses

Inspect descriptive statistics while retaining outliers.
Compare sample and population variance with an explicit missing-field policy.

How to use it

1.Enter supported decimal values separated by commas, semicolons or newlines.
2.Select population or sample variance and reject or skip missing fields, then calculate.
3.Inspect count, skipped fields, exact fractions, rounded decimals, modes and the variance definition.

Statistics examples

Population and sample variance

2,4,4,4,5,5,7,9

n=8; Mean=5; Median=9/2; Modes (numeric order)=4; Population (divide by n): Variance=4; Sample (divide by n − 1): Variance=32/7

For 2,4,4,4,5,5,7,9, n=8, mean=5, median=9/2, mode=4 with frequency3, range=7. Population variance=4 and standard deviation=2; sample variance=32/7 and standard deviation rounds to2.138089935299.

Large adjacent values

1000000000000000000,1000000000000000001,1000000000000000002

Mean=1000000000000000001; Population (divide by n): Variance=2/3; Standard deviation=0.816496580928

The mean is exactly1000000000000000001 and population variance is2/3, despite the large common offset. The standard deviation rounds to0.816496580928.

Limits and notes

Separate values with commas, semicolons or newlines. Up to 1,000 fields and 64,000 characters; each value allows an optional minus, 30 integer digits and 12 fractional digits. Use a decimal point. Exponents, expressions and thousands separators are not supported. A comma always separates fields: 1,000 means the two values 1 and 0, not one thousand.
Missing means an empty field, NA, N/A or null (case insensitive), including leading or trailing separators. Other invalid values are always rejected. Skipped fields are counted.
Mean, median, range and variance retain exact fractions. Standard deviation is shown as a rounded decimal and may be irrational. Modes use numeric equality; a set with no repetitions has no mode. Outliers are retained.
Browser-local only. No upload, saved history or expression execution.

Frequently asked questions

Which variance definition should I select?

Population variance divides the sum of centered squares by n; sample variance divides by n−1 and is unavailable for one valid value. Choose based on what the entered list represents.

What counts as missing?

Missing means an empty field, NA, N/A or null (case insensitive), including leading or trailing separators. Other invalid values are always rejected. Skipped fields are counted.

Are all displayed decimals exact?

Mean, median, range and variance retain exact fractions. Standard deviation is shown as a rounded decimal and may be irrational. Modes use numeric equality; a set with no repetitions has no mode. Outliers are retained.