Average Calculator — Mean, Median, Mode
Calculate the mean, median, mode, range, and standard deviation of any set of numbers. Enter values separated by commas or on separate lines.
Mean (Average)
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Frequently Asked Questions
- Mean = Sum of all values ÷ Count of values. Example: the mean of 4, 8, 15, 16, 23, 42 = 108 ÷ 6 = 18. The mean is the most common measure of central tendency, but it can be skewed by extreme outliers. For skewed data, the median is often a better measure.
- Mean: arithmetic average (sum ÷ count). Median: the middle value when sorted — not affected by outliers. Mode: the most frequently occurring value. Example: dataset [1, 2, 2, 3, 100] → Mean = 21.6, Median = 2, Mode = 2. The median (2) better represents the typical value here.
- Sort the values in ascending order. If odd count: median = middle value. If even count: median = average of two middle values. Example: [3, 5, 7, 9] → median = (5+7)/2 = 6. Example: [3, 5, 7] → median = 5.
- Geometric mean = n-th root of (x₁ × x₂ × … × xₙ). It's used when values multiply together, such as growth rates, investment returns, or ratios. Example: An investment grows 10%, then 50%, then −20% → Geometric mean = ∛(1.10 × 1.50 × 0.80) − 1 = 9.14% average annual return.
- Standard deviation (SD) measures how spread out values are from the mean. Low SD = values clustered near mean. High SD = widely spread values. Formula (population): σ = √(Σ(x−μ)²/N). Formula (sample): s = √(Σ(x−x̄)²/(N−1)). In a normal distribution, ~68% of values fall within 1 SD of the mean.
- Weighted average = Σ(value × weight) ÷ Σ(weights). Example: Exam grades 80 (worth 30%), 90 (worth 30%), 70 (worth 40%) → Weighted avg = (80×0.30 + 90×0.30 + 70×0.40) ÷ 1.0 = (24 + 27 + 28) = 79. Different from simple average (80) because weights differ.
- If the percentages refer to parts of the same base, use a simple average. If they refer to different bases (e.g., different sample sizes), use a weighted average based on the sample sizes. Example: a class of 20 scored 80% and a class of 30 scored 90% → true average = (20×80 + 30×90) ÷ 50 = 86%, not (80+90)/2 = 85%.
- Range = Maximum value − Minimum value. It's the simplest measure of spread. Example: dataset [3, 7, 11, 15, 19] → Range = 19 − 3 = 16. The range is easy to calculate but sensitive to outliers. The interquartile range (IQR = Q3 − Q1) is a more robust spread measure for skewed data.