Statistics Calculator

What this calculator does

This calculator computes key descriptive statistics for a set of numbers: mean (average), median (middle value), mode (most frequent value), standard deviation, variance, range, sum, and count. Enter your data set and get a complete statistical summary instantly.

Descriptive statistics are the foundation of data analysis. Before running complex models or making decisions, you need to understand the basic shape and spread of your data. These measures tell you what is typical (central tendency), how spread out the values are (dispersion), and whether there are patterns or outliers worth investigating.

This tool is useful for students working through statistics coursework, researchers summarizing experimental data, business analysts reviewing performance metrics, and anyone who needs a quick numerical summary of a data set.

How to use it

1. Enter your data as a comma-separated list of numbers (e.g. 12, 15, 18, 22, 22, 25, 30).
2. The calculator automatically computes all statistics.
3. Review the mean, median, mode, standard deviation (population and sample), variance, range, min, max, sum, and count.

Formulas used

• Mean (average): μ = Σxᵢ / n Sum all values and divide by the count.

• Median: Sort the data. If n is odd, the median is the middle value. If n is even, it is the average of the two middle values.

• Mode: The value(s) that appear most frequently. A data set can have no mode, one mode, or multiple modes.

• Range: Max − Min

• Variance: Population variance: σ² = Σ(xᵢ − μ)² / n Sample variance: s² = Σ(xᵢ − x̄)² / (n − 1) The sample variance uses n−1 (Bessel's correction) to provide an unbiased estimate when the data is a sample from a larger population.

• Standard deviation: σ = √(variance) Measures the average distance of each data point from the mean.

Examples

Example 1 — Test scores: Data: 78, 85, 90, 92, 88, 76, 95, 85, 82, 89. Mean = 86.0. Median = 86.5. Mode = 85. Std dev (sample) ≈ 5.98. Range = 19.

Example 2 — Monthly sales: Data: 12000, 15500, 13200, 18000, 14700, 16100. Mean = $14,917. Median = $14,850. No mode. Std dev ≈ $2,038. Range = $6,000.

Example 3 — Small data set with outlier: Data: 5, 7, 6, 8, 6, 7, 42. Mean = 11.57 (pulled up by outlier). Median = 7 (not affected by outlier). Mode = 6, 7. This illustrates why median is often preferred when outliers are present.

Tips and common mistakes

• Mean vs. median: The mean is sensitive to outliers; the median is not. For skewed data (incomes, house prices, response times), the median is usually more representative of the "typical" value.
• Population vs. sample standard deviation: Use population (÷ n) when your data set is the entire population. Use sample (÷ n−1) when your data is a sample from a larger group, which is the more common case in practice.
• Mode may not exist or may have multiple values. It is most useful for categorical or discrete data (e.g. survey responses, shoe sizes).
• Standard deviation has the same units as your data. Variance is in squared units, which is harder to interpret directly. Standard deviation is usually the more practical measure of spread.
• Check for data entry errors. A single mistyped value (e.g. 420 instead of 42) can dramatically affect the mean and standard deviation. Always review your input.
• Small sample sizes produce less reliable statistics. Be cautious drawing conclusions from fewer than 30 data points.