Statistics
Mean, median, mode calculator
Paste a list of numbers (comma, space, or newline separated). The calculator returns the arithmetic mean, the median, the mode (or modes if tied), and basic descriptives — count, sum, min, max, range.
Formula
Three different 'averages' that often disagree, especially in skewed data:
• **Mean** is the arithmetic average — sum divided by count. Sensitive to outliers (one billionaire skews mean income upward). • **Median** is the middle value when data is sorted. Robust to outliers — half of values are above, half below. • **Mode** is the most frequent value. Useful for categorical or discrete data, less useful for continuous measurements where exact repeats are rare.
For symmetric distributions (heights, IQs) all three converge. For skewed distributions (incomes, house prices, file sizes) they diverge — median is usually the most representative.
Examples
- 014, 8, 15, 16, 23, 42→ Mean 18, Median 15.5, no mode (all unique). Sum 108, range 38.
- 021, 2, 2, 3, 4, 4, 4, 5→ Mean 3.125, Median 3.5, Mode 4 (appears 3×)
- 0310, 10, 20, 30→ Mean 17.5, Median 15, Mode 10 (2×)
- 041, 2, 3, 1000 (outlier)→ Mean 251.5 (skewed), Median 2.5 (robust)
FAQ
- Mean for symmetric data without outliers, or when you need every value to contribute (e.g. computing total). Median for skewed data, ordinal data, or when outliers would distort a result (income, house prices, response times).