Mean, Median, Mode & Range Calculator

All three measure central tendency but answer slightly different questions. The mean is the arithmetic average — sum divided by count. The median is the middle value of the sorted dataset. The mode is the most frequently occurring value. For perfectly symmetric data they coincide; for skewed data they spread apart, and the difference between them is often the most informative thing about the distribution.

Use the median whenever your data contains outliers or is heavily skewed. The classic examples are income (one billionaire skews the mean massively but barely moves the median), house prices, response times, and delay distributions. The mean is pulled toward extreme values; the median always sits at the 50th percentile and is unaffected. For symmetric, well-behaved data (heights, exam scores, measurement noise) the mean is fine and slightly more efficient.

Range is simply max − min — the full extent of the data. IQR (interquartile range) is Q3 − Q1, the spread of the middle 50%. IQR is robust to outliers (it only sees the middle of the distribution), while range is extremely sensitive — a single extreme value can dominate it. Box plots use the IQR; range is most useful for a quick rough sense of "how spread out are these numbers?"

Yes. If two or more values share the highest frequency the dataset is called bimodal, trimodal, or multimodal. If every value occurs exactly once there is no mode (no value is more frequent than any other). This calculator returns all modes when there is a tie, and reports "None" when the data has no repeated values.

The geometric mean is the nth root of the product of n values: (x₁ × x₂ × … × xₙ)^(1/n). It is the correct average for ratios, growth rates, and any multiplicative data — compound interest returns, population growth, performance ratios. For positive data the geometric mean is always less than or equal to the arithmetic mean (this is the AM-GM inequality), and equal only when all values are identical.

The harmonic mean is n ÷ Σ(1/xᵢ) — the reciprocal of the arithmetic mean of reciprocals. It is the correct average for rates over equal distances: average speed over multiple legs of a journey, average price-per-share when buying equal-dollar amounts of stock, etc. It is always less than or equal to both the arithmetic and geometric means and is pulled toward the smallest values.

Sort the data, then Q1 is the value at position (n+1) × 0.25, Q2 is the median, and Q3 is at (n+1) × 0.75 — interpolating between two ranks if the position falls between them. Different software packages use slightly different methods (R has nine!); this calculator uses the linear-interpolation method (R type 6, the most common textbook convention). Differences across methods are usually small (under 5% of IQR) for n > 20.

IQR (Interquartile Range) is Q3 − Q1 — the spread of the middle 50% of the data. It is the standard robust measure of spread and the basis of the 1.5 × IQR rule for identifying outliers (any point below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged). IQR is what box plots visualise (the box itself spans Q1 to Q3, with the median as a line inside).

Any combination of commas, spaces, tabs, or new lines works. So 1, 2, 3, 4, 1 2 3 4, and one number per line all parse correctly. You can paste directly from Excel or Google Sheets (which produces tab-separated values). Non-numeric tokens are ignored. Negative numbers and decimals are supported.

A distribution is skewed when one tail is longer than the other. Right-skewed (positive skew): long tail to the right, mean > median (income, house prices). Left-skewed (negative skew): long tail to the left, mean < median (exam scores when most students do well, age at death). The relationship mean > median or mean < median is a quick visual diagnostic for skew. For heavily skewed data, prefer median + IQR over mean + standard deviation.

Not directly — this calculator expects a flat list of raw values. For grouped frequency data, expand each group out (e.g. "5 appears 3 times" → enter 5, 5, 5). For weighted means with arbitrary weights, use a dedicated weighted-mean calculator or compute Σ(wᵢ × xᵢ) ÷ Σwᵢ by hand. The "Weighted Mean" row in older versions of this tool was identical to the arithmetic mean since all weights were equal — we removed it to avoid confusion.

All calculations use IEEE 754 double-precision arithmetic, accurate to about 15 decimal digits. For school, university, and professional data analysis this is far more precision than your input data warrants. Geometric mean computation handles the product overflow risk by transforming into log-space internally for large datasets. Median, mode, and quartiles are exact (no floating-point rounding).