Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance. Variance is harder to interpret directly but is used extensively in statistical calculations.

How do I enter numbers in this statistics calculator?

Paste or type numbers separated by commas, spaces, or new lines. For example: 5, 10, 15, 20 or one number per line. The calculator parses any combination of these delimiters automatically.

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Statistics Calculator

Q: What is the difference between mean, median, and mode?

Mean is the arithmetic average (sum ÷ count). Median is the middle value when numbers are sorted — it is resistant to outliers. Mode is the most frequently occurring value. For skewed data, median is often more useful than mean.

Q: What is standard deviation?

Standard deviation measures how spread out numbers are from the mean. A low standard deviation means values cluster near the mean; a high one means values are widely spread. Formula: √(Σ(xi − mean)² ÷ n) for population standard deviation.

Q: What is the range in statistics?

Range = Maximum value − Minimum value. It gives a quick sense of how spread out the data is but is sensitive to outliers. A single extreme value can make the range misleadingly large.

Q: What is the difference between population and sample standard deviation?

Population standard deviation (σ) divides by n; sample standard deviation (s) divides by n−1 (Bessel's correction). Use population when you have data for the entire group; use sample when your data is a subset of a larger population.

Paste any list of numbers to instantly get mean, median, mode, range, variance, standard deviation, min, max, and more.

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Frequently Asked Questions

What is the difference between mean, median, and mode?

Mean = sum ÷ count (arithmetic average). Median = middle value when sorted (resistant to outliers). Mode = most frequent value. For skewed datasets, median is often more representative.

What is standard deviation?

Standard deviation measures how spread out values are from the mean. Low SD = values cluster near the mean. High SD = values are widely spread. Formula: √(Σ(xi − mean)² ÷ n).

What is variance?

Variance = average of squared differences from the mean. Standard deviation is just √variance. Variance is less intuitive but widely used in statistical inference.

What is the range in statistics?

Range = max − min. Quick measure of spread but sensitive to outliers — a single extreme value makes range misleadingly large.

What is the difference between population and sample standard deviation?

Population SD divides by n; sample SD divides by n−1 (Bessel's correction). Use population when you have all data; use sample when your dataset is a subset.

How do I enter numbers in this calculator?

Type or paste numbers separated by commas, spaces, or new lines. Any combination works — the calculator auto-parses all delimiters.

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