Statistics Calculator

Enter a list of numbers (comma, space, or newline separated) to compute descriptive statistics instantly.

Data Input
Enter numbers above to compute statistics.

How to Use the Statistics Calculator

  1. Paste or type numbers into the input box. Use commas, spaces, or newlines to separate them.
  2. Choose sample or population mode using the chips — this affects standard deviation and variance.
  3. See all statistics instantly — the calculator updates as you type.
  4. Review the box plot and histogram to understand your data's distribution visually.
  5. Copy or download your results for use in reports or spreadsheets.

Descriptive Statistics Explained

Measures of Central Tendency

Mean (average): The sum of all values divided by the count. Sensitive to outliers — a single extreme value can pull the mean far from the typical value. Formula: μ = Σx / N.

Median: The middle value when sorted. For an even count, it's the average of the two middle values. Robust to outliers — useful for skewed distributions like income data or house prices.

Mode: The most frequently occurring value(s). A dataset can be unimodal (one mode), bimodal (two modes), or multimodal (many modes). Useful for categorical-like data and survey responses.

Measures of Spread

Range: Max minus Min. A simple but crude measure of spread, highly sensitive to outliers.

Variance: The average of squared differences from the mean. Squaring emphasizes larger deviations and produces a value in squared units. Formula (sample): s² = Σ(x - x̄)² / (N-1).

Standard Deviation: The square root of variance, in the same units as the original data. Approximately 68% of data in a normal distribution falls within ±1 standard deviation of the mean (empirical rule).

Interquartile Range (IQR): Q3 minus Q1. Measures the spread of the middle 50% of data. Used to identify outliers: values beyond Q1 - 1.5×IQR or Q3 + 1.5×IQR are typically considered outliers.

The Box Plot

The box plot (or box-and-whisker plot) visualizes five key statistics: minimum, Q1, median, Q3, and maximum. The box represents the IQR (middle 50% of data). The line inside the box is the median. Whiskers extend to the min and max (or to the furthest non-outlier). Box plots are excellent for comparing distributions across multiple groups.

Percentiles

Percentiles tell you the value below which a given percentage of the data falls. The 25th, 50th, and 75th percentiles (Q1, Q2/median, Q3) are quartiles. P90 means 90% of values are below that number. Percentiles are widely used in healthcare (growth charts), education (test scores), and performance benchmarking. For generating test data to analyze, try the Random Number Generator.

Frequently Asked Questions

Population standard deviation (σ) divides by N and is used when you have data for every member of a group. Sample standard deviation (s) divides by N-1 (Bessel's correction) and is used when your data is a sample from a larger population. For small samples, the sample std dev gives a less biased estimate.
The median is the middle value when sorted. For an odd count it's the exact middle element; for an even count it's the average of the two middle elements. For example, the median of [1, 3, 5, 7] is (3+5)/2 = 4.
The mode is the most frequently occurring value. If multiple values share the highest frequency, all are listed as modes (multimodal). If all values appear exactly once, the dataset has no mode.
This calculator uses linear interpolation. For example, the 25th percentile (Q1) is the value below which 25% of the data falls. The 50th percentile equals the median.
Numbers can be separated by commas, spaces, tabs, or newlines. The calculator ignores empty entries and non-numeric text. For example: "1, 2, 3" or "1 2 3" or one number per line all work.