Measures of Variability Calculators
This page presents tools that summarise how widely data values differ from central points, providing numerical measures that describe spread, shape and distribution consistency.
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Empirical Rule Calculator
A normal (bell-shaped) distribution often places most values within one, two, or three standard deviations of the mean.
Example use: checking how far a set of daily commute times tends to fall from its average.
Inputs: data values, standard deviation type
Outputs: count, sum, mean, variance, standard deviation, coefficient of variation, skewness, excess kurtosis, minimum z-score, maximum z-score, one-standard-deviation range, two-standard-deviation range, three-standard-deviation range, full range, theoretical percentages, actual count, actual percentages
Visual: a normal distribution curve with markers showing one, two, and three standard deviations from the mean
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Interquartile Range Calculator
A dataset divided into four equal parts highlights how values cluster around the median and how widely the middle half is spread.
Example use: comparing the middle spread of recorded room temperatures across several days.
Inputs: data values, interpolation method, quartile inclusion method
Outputs: total count, minimum, first quartile, median, third quartile, maximum, interquartile range, semi-interquartile range, lower outlier bound, upper outlier bound, coefficient of quartile variation, full range, mean average
Visual: a bar display of quartile positions and a box-and-whisker layout showing the middle range and possible outliers
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Kurtosis Calculator
A distribution's shape can be described by how sharply it peaks and how heavy its tails are compared with a normal curve.
Example use: checking whether a set of household electricity readings has unusually frequent extreme values.
Inputs: data values, kurtosis type
Outputs: dataset size, arithmetic mean, coefficient of variation, sample standard deviation, sample skewness, standard error of skewness, sample excess kurtosis, standard error of kurtosis, population standard deviation, population skewness, population excess kurtosis, Jarque-Bera statistic, Jarque-Bera p-value, distribution shape
Visual: a histogram of the data with a smooth normal curve drawn for comparison
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Root Mean Square Calculator
A set of values can be summarised by a root-mean-square measure that reflects both their size and their variation.
Example use: assessing the overall level of sound readings taken throughout a day in a living room.
Inputs: data values
Outputs: total count, arithmetic mean average, rectified mean, sum of squares, mean of squares, standard deviation, peak magnitude, root-mean-square value, crest factor, form factor
Visual: a display of data points with lines marking the root-mean-square level and the arithmetic mean
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Skewness Calculator
A distribution may lean to one side when its values extend further in one direction than the other, creating measurable skewness.
Example use: checking whether recorded shower durations tend to run longer on one side of the average.
Inputs: data values, skewness type
Outputs: mean, median, Pearson's first skewness, Bowley's skewness, standard deviation, skewness, excess kurtosis, skewness z-score, kurtosis z-score, bimodality coefficient, distribution shape
Visual: a histogram with a normal curve and a line marking the mean
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Standard Deviation Calculator
A dataset's spread around its mean can be summarised by a standard deviation that reflects how far typical values lie from the centre.
Example use: measuring how much a person's daily water intake varies across a month.
Inputs: data values, standard deviation type
Outputs: standard deviation, mean, variance, coefficient of variation, margin of error, sum, count, range
Visual: a display of data values with their frequencies, the mean line, and a smooth normal curve showing the overall distribution
Measures of Variability FAQs
Standard deviation summarises how far values typically sit from the mean, with larger values indicating wider overall dispersion.
The interquartile range reflects the spread of the central half of the data, reducing the influence of unusually high or low values.
Skewness describes distribution asymmetry, while kurtosis reflects tail heaviness and the prominence of central peaks.
The empirical rule estimates proportions within one, two and three standard deviations when data approximates a normal pattern.
Root mean square summarises the typical magnitude of varying values, combining squared contributions before averaging and taking the square root.