Averages calculators
Calculators for every kind of average: the mean, median and mode of a list or frequency table, weighted averages, and the geometric, harmonic and quadratic means for growth rates, speeds and signals. There are also ready-made tools for everyday averages such as grades, star ratings and batting averages.
Which calculator do I need?
| You have or want | Use |
|---|---|
| A list of numbers and you want the ordinary average | Mean (average) calculator |
| Mean, median, mode and range together, for homework | Mean, median, mode & range |
| Data with an extreme value, such as incomes or house prices | Median calculator |
| Values that count for different amounts, such as weighted marks | Weighted average calculator |
| Growth rates or returns over several periods | Geometric mean calculator |
| Rates such as speeds over equal distances | Harmonic mean calculator |
| A frequency table or class intervals | Mean calculator (series and grouped data) |
| The mean is known but one value or frequency is missing | Missing value and missing frequency |
Mean, median and mode
The three standard measures of the centre, from a plain list, a frequency table or grouped data.
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Mean (average) calculator
The mean of a list with the sum and count, plus the median, mode and SD.
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Arithmetic mean calculator
Σx ÷ n for a list or frequency table, with every step and the GM and HM for comparison.
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Mean calculator (series and grouped data)
The arithmetic mean of a list, a frequency table or class intervals, by the direct, assumed-mean or step-deviation method.
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Median calculator
The middle value of a list, sorted and worked for odd and even counts.
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Mode calculator
The mode of a list, a frequency table or grouped data, including the grouping method.
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Median and mode calculator (grouped data)
Median and mode of a list, a discrete series or class intervals, checked with Mode = 3 Median − 2 Mean.
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Mean, median, mode & range
Mean, median, mode and range of a list in one pass.
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Mean, median, mode and range calculator
All four from a list, with the working for each and every mode reported.
Weighted averages
When some values count for more than others, as with course weightings, portfolio shares or survey weights.
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Weighted average calculator
Σwx ÷ Σw for marks, prices or any weighted values, including GPA-style grades.
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Weighted mean calculator
Σwx ÷ Σw with the full table: the weighted arithmetic mean used for index numbers and cost-of-living figures.
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Weighted median calculator
The value where the cumulative weight reaches half, with the exact-half tie handled.
Other means
Averages built for particular kinds of data: products and growth, rates, magnitudes and quick estimates.
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Geometric mean calculator
The nth root of the product, or the average compound growth rate from percentages.
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Harmonic mean calculator
The average for rates, such as speeds over equal distances, with a weighted version for unequal ones.
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Root mean square calculator
The quadratic mean √(Σx² ÷ n), used for AC signals, errors and magnitudes.
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Midrange calculator
The midpoint of the smallest and largest values, compared with the mean and median.
Everyday averages and missing values
Ready-made averages for grades, ratings and sport, and a solver for a missing value when the mean is known.
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Grade average calculator
The mean and median of your grades, what dropping the lowest does, and their SD.
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Average rating calculator
Average star rating from the count at each score, with a Bayesian average and the distribution.
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Batting average calculator
Batting average from hits and at-bats, printed the box-score way (.281), with its standard error.
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Missing value and missing frequency calculator
Find a missing observation, or one or two missing frequencies, when the mean is known.
Choosing an average
An average is a single number that stands for a whole set, and different questions need different ones. The arithmetic mean uses every value and is the right default for roughly symmetric data. The median is the middle value once the data are sorted, so a few extreme values cannot pull it around. The mode is the most frequent value and the only average that works for categories such as shoe brands or blood types.
Take 2, 3, 3, 5, 7, 40. The mean is 60 ÷ 6 = 10, but five of the six values are below it. The median is 4 and the mode is 3. When the mean and median disagree this much, the data are skewed and the median is the better summary.
When the ordinary mean gives the wrong answer
- Growth rates. An investment that gains 10% one year and loses 10% the next has an arithmetic mean return of 0%, but it has lost money: 1.1 × 0.9 = 0.99. The geometric mean gives the true average rate, √0.99 − 1 ≈ −0.50% a year.
- Speeds and other rates. Drive one leg at 60 km/h and an equal-length return at 40 km/h and your average speed is not 50 but the harmonic mean, 2 ÷ (1/60 + 1/40) = 48 km/h, because you spend longer at the slower speed.
- Unequal importance. If coursework is worth 30% and the exam 70%, a plain mean of the two marks is wrong. Use the weighted average.
For any set of positive numbers the three Pythagorean means always fall in the same order: harmonic ≤ geometric ≤ arithmetic, with equality only when every value is the same.
Grouped data
With a frequency table of exact values, the mean is Σfx ÷ Σf and matches the raw-data answer. With class intervals the calculators use class midpoints, so the grouped mean and the grouped median and mode are estimates. If you know the mean but a value or frequency is missing, the missing value calculator solves for it.