Measures of Central Tendency Calculators
This page presents tools that summarise datasets with single central values, covering several average types and related numerical descriptions.
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Arithmetic Mean Calculator
A collection of values has a central level that can be described by its average, middle value, most frequent value, total, amount of entries, and overall spread.
Example use: estimating the typical number of steps taken across several short walks.
Inputs: list of numbers
Outputs: average, middle value, most frequent value, total of all values, number of entries, highest minus lowest
Visual: bar chart with a smooth line showing short-term movement, and a dashed line marking the average level
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Geometric Mean Calculator
A group of positive values has a multiplicative central level that differs from the usual average and highlights how values combine through repeated proportional changes.
Example use: comparing several daily ratios when checking how much a plant's height increases each day.
Inputs: numbers separated by commas
Outputs: geometric mean, average, number of entries, highest value, lowest value, step-by-step working, final geometric mean
Visual: bar chart showing individual and grouped values, a dashed line marking the geometric mean, and a smooth line showing short-term movement
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Harmonic Mean Calculator
Rates or positive values that relate to repeated equal portions have a central level that is influenced most strongly by the smaller entries.
Example use: combining several walking speeds recorded over equal distances.
Inputs: positive numbers separated by commas
Outputs: harmonic mean, average, number of entries, highest value, lowest value
Visual: bar chart showing each value and a line marking the harmonic mean
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Trimmed Mean Calculator
A set of values can have its extreme entries removed on both ends to give a central level that reduces the influence of unusually high or low points.
Example use: estimating a typical reading time after removing unusually fast and unusually slow attempts.
Inputs: numbers separated by commas or spaces, trim percentage
Outputs: trimmed mean, original average, trimmed percentage on each side, number of values removed on each side, remaining number of entries, total of remaining values
Visual: bar chart showing the sorted values with a line marking the trimmed mean
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Trimean Calculator
The trimean summarises a set of values by taking a weighted average of the lower quartile, median, and upper quartile, giving a balanced measure of central tendency.
Example use: summarising several recorded bedtimes across a week.
Inputs: numbers separated by commas or spaces
Outputs: trimean, lower quarter point, middle value, upper quarter point, number of entries
Visual: bar chart showing the sorted values with lines marking the trimean and the middle value
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Weighted Mean Calculator
A collection of values can be combined into a central level that gives different importance to each entry according to its assigned weight.
Example use: combining several reading scores where some tasks count more than others.
Inputs: data values and their weights
Outputs: weighted mean, total of weights, total of weighted values, number of entries, highest value, lowest value, range
Visual: bar chart showing each value with weight details on hover, plus lines marking the weighted mean and the usual average
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Winsorised Mean Calculator
A set of values can have its extreme entries replaced rather than removed, producing a central level that limits the effect of unusually high or low points.
Example use: estimating a typical commute time after adjusting unusually long and unusually short journeys.
Inputs: numbers separated by commas or spaces, winsorising percentage
Outputs: winsorised mean, original average, winsor percentage on each side, values replaced on each side, number of entries, total of the adjusted set
Visual: bar chart showing the adjusted values with a line marking the winsorised mean
Central Tendency FAQs
A measure of central tendency summarises a dataset with a single value representing its middle or typical position.
A trimmed average is used when extreme values influence the standard average, reducing their effect by removing fixed proportions from each end of the dataset.
The Winsorised average limits the influence of extreme values by adjusting them rather than excluding any observations, providing a more stable central estimate.