Mean, Median, Mode & Range Calculator
Calculate mean, median, mode, range, and more descriptive statistics from any dataset.
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Get the mean, median, mode, and range for any dataset, along with the geometric and harmonic means and a full frequency breakdown of every value entered.
How Mean, Median, Mode & Range Calculator Works
Mean is the familiar arithmetic average (sum ÷ count). Median is the middle value once the data is sorted in order (or the average of the two middle values when there's an even number of entries), which makes it far less sensitive to extreme outliers than the mean. Mode is whichever value (or values) occur most often, and the calculator reports "no mode" whenever every value in the set is unique.
Range is simply the maximum value minus the minimum, the simplest possible measure of how spread out the data is. The frequency table beneath the results lists exactly how many times each distinct value appears, plus its rank position within the sorted list.
Geometric mean — the nth root of the product of all n values — is only defined when every value is positive, and is the mathematically correct way to average growth rates, ratios, or percentages that compound over time (like annual investment returns). Harmonic mean — n divided by the sum of the reciprocals of every value — is the appropriate average for rates measured over a fixed quantity, such as speeds traveled over equal distances.
See It In Action
Who Uses Mean, Median, Mode & Range Calculator and Why
- Getting a quick central tendency summary (mean, median, mode, range) for a small classroom or survey dataset.
- Correctly averaging a series of annual investment growth rates using the geometric mean instead of a plain average.
- Finding the true average speed over equal distances traveled at different speeds using the harmonic mean.
- Identifying which values repeat most often in a multimodal dataset using the frequency breakdown.
Mistakes to Avoid
- Using the arithmetic mean to average growth rates, ratios, or percentages that compound over time — the arithmetic mean overstates true average growth in these cases, where geometric mean is correct.
- Using the arithmetic mean for average speed over equal distances at different speeds — the harmonic mean is the mathematically correct choice for that specific rate-over-fixed-base scenario.
- Expecting a geometric or harmonic mean result when the dataset contains a zero or negative value — both require every value to be positive.
Tips for Best Results
- Reach for the geometric mean whenever you're averaging values that multiply or compound over time, such as a series of yearly growth rates.
- Reach for the harmonic mean whenever you're averaging a rate measured over a fixed distance or base, such as speed over equal-length trips.
Fixing Common Problems
Geometric or harmonic mean shows as unavailable. — Check your dataset for a zero or negative value — both means require every value to be positive, since they rely on logarithms or reciprocals that are undefined otherwise.
Terms Explained
Geometric mean: The nth root of the product of n values, the mathematically correct way to average growth rates, ratios, or percentages that compound.
Harmonic mean: N divided by the sum of the reciprocals of n values, the correct average for rates measured over a fixed quantity, like speed over equal distances.