statistics.js

Computes the arithmetic mean of the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error. mean() is an alias of this method.

var mean = stats.arithmeticMean([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

4.69230…

Computes the cubic mean of the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var mean = stats.cubicMean([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

6.28600…

Computes the Gastwirth-Cohen mean of the values in a dataset data that can be either the name of a column (string) or an array of values. The Gastwirth-Cohen mean is defined as the weighted mean of three quantils:

• the lambda-weighted alpha quantil
• the (1 - alpha)-quantil and
• the (1 - 2 * lambda)-weighted median

alpha and lambda must be within the range of [0, 0.5]. If the scale of measure of the column given by data is not ordinal or of higher order or if alpha or lambda are outside of the range of [0, 0.5], it will return undefined and throw an error.

var mean = stats.gastwirthCohenMean([1, 3, 7, 4, 12, 4, 6, 7, 1, 2], { alpha: 0.3, lambda: 0.1 });

4.1

Computes the geometric mean of the values in a dataset data that can be either the name of a column (string) or an array of values. If any non-positive values are supplied, this method will return undefined. If the scale of measure of the column given by data is not metric, it will return undefined and throw an error.

var mean = stats.geometricMean([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);
var meanWithInvalids = stats.geometricMean([0, 3, -12, 7, 9, 4, 1]);

mean: 3.74447…
meanWithInvalids: undefined

Computes the harmonic mean of the values in a dataset data that can be either the name of a column (string) or an array of values. Returns 0 if any of the values are also 0. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var mean = stats.harmonicMean([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

2.82901…

Retrieves the median of a dataset data that can be either the name of a column (string) or an array of values.

var median = stats.median([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

4

Computes the mid-range of a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var midRange = stats.midRange([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

6.5

Retrieves the most frequent value in a dataset data that can be either the name of a column (string) or an array of values. If there are two or more most common values of equal frequency, an array with these values will be returned.

var mode = stats.mode([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

[4, 7]

Computes the root mean square of the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var mean = stats.rootMeanSquare([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

5.54006…

Computes the Winsorised (truncated) mean of the values in a dataset data that can be either the name of a column (string) or an array of values. Note, that for every truncated value of the sorted list, the now most extreme value will be repeated in its place, e.g. in a 10% truncated list of twenty values both the originally third and the 18^th value in order will be repeated twice in order to replace the truncated first, second and 19^th and 20^th values, respectively. It’s commonly used to discard outliers that are within the outermost percentage per cent of values on either end of the full range. percentage must be an integer or floating point number within the range of [0, 0.5]. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var mean = stats.winsorisedMean([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2], 0.33);

4.38461…

The coefficient of variation is a relative parameter of dispersion that expresses the standard deviation relative to the expected value of a statistical variable. This allows for comparison of variables with significantly diverse expected values. Thus, it is similar to the index of dispersion. The expected value can either be supplied as an additional input parameter or will be substituted by the arithmetic mean. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var coeffVar = stats.coefficientOfVariation([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

0.65330…

Counts the number of values in a dataset data that can be either the name of a column (string) or an array of values that smaller or equal to boundary. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var frequency = stats.cumulativeFrequency([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2], 6);

9

Sorts the values in a dataset data that can be either the name of a column (string) or an array of values in descending order and returns them with their absolute and relative (in the range of 0 and 1) frequencies.

var frequencies = stats.frequencies(["male", "female", "male", "male", "female", "female", "indeterminate", "female"]);

[
	{ value: "female", absolute: 4, relative: 0.5 },
	{ value: "male", absolute: 3, relative: 0.375 },
	{ value: "indeterminate", absolute: 1, relative: 0.125 }
]

Computes the geometric standard deviation of the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var stdDev = stats.geometricStandardDeviation([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

2.05493…

The index of dispersion is a relative parameter of dispersion that expresses the variance relative to the expected value of a statistical variable. This allows for comparison of variables with significantly diverse expected values. Thus, it is similar to the coefficient of variation. The expected value can either be supplied as an additional input parameter or will be substituted by the arithmetic mean. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var indexDisp = stats.indexOfDispersion([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

2.00273…

Computes the interquartile range of a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var interQuartileRange = stats.interQuartileRange([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

4

Finds the largest among the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var min = stats.maximum([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

12

Computes the median absolute deviation of the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var medDev = stats.medianAbsoluteDeviation([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

2

Finds the smallest among the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var min = stats.minimum([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

1

Computes the quantiles of the values in a dataset data that can be either the name of a column (string) or an array of values. The percentage should be given as an integer or floating point number between 0 and 1. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var quantile = stats.quantile([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2], 0.33);

3

Computes the quartiles of the values in a dataset data that can be either the name of a column (string) or an array of values and returns them as an array with the lower quartile at the 0^th index and the higher quartile at the 1^st index. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var mode = stats.quartiles([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

[3, 7]

Computes the range of the values in a dataset data that can be either the name of a column (string) or an array of values, defined as the difference of their maximum and their minimum. If the scale of measure of the column given by data is nominal, it will retrieve an array of all the unique values in the dataset instead.

var range = stats.range([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

11

Computes the standard deviation of the values in a dataset data that can be either the name of a column (string) or an array of values. By default, the arithmetic mean is computed for and Bessel’s correction is applied. This is the best option if the true arithmetic mean within the population is a priori unknown and can only be approximated by the arithmetic mean of the sample. If corrected is set to false, Bessel’s correction will not be applied, effectively computing the population variance with an unknown arithmetic mean. If corrected is set to an integer or a floating point number, this will be used as the true mean and Bessel’s correction will not be applied. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var variance = stats.standardDeviation([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

3.06552…

Computes the variance of the values in a dataset data that can be either the name of a column (string) or an array of values. By default, the arithmetic mean is computed for and Bessel’s correction is applied. This is the best option if the true arithmetic mean within the population is a priori unknown and can only be approximated by the arithmetic mean of the sample. In that case, the numerically stable Welford’s method is used which yields a correct result even for very large datasets and very large numbers. If corrected is set to false, Bessel’s correction will not be applied, effectively computing the population variance with an unknown arithmetic mean. If corrected is set to an integer or a floating point number, this will be used as the true mean and Bessel’s correction will not be applied. If the scale of measure of the column given by data is not interval or of higher order, it will return undefined and throw an error.

var variance = stats.variance([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

9.39743…

Computes the excess kurtosis of the values in a dataset data that can be either the name of a column (string) or an array of values. This measure was introduced to compare the shape of a distribution to that of the normal distribution. It is defined as the kurtosis and can make three basic descriptions:

• (mesokurtic): the bell shape of the normal distribution
• (leptokurtic): a more slender and steep shape
• (platykurtic): a more flat and wide shape

If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var excess = stats.excessKurtosis([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

-0.05486…

Computes the kurtosis of the values in a dataset data that can be either the name of a column (string) or an array of values. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var kurtosis = stats.kurtosis([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

2.94513…

Computes the sample skewness of the values in a dataset data that can be either the name of a column (string) or an array of values. There are several definitions of skewness, however this toolkit uses the sample skewness if populationSkewness is set to false and the adjusted Fisher-Pearson standardised moment coefficient for the sample skewness if it’s set to true. If the scale of measure of the column given by data is not ordinal or of higher order, it will return undefined and throw an error.

var skewness = stats.skewness([1, 3, 7, 4, 12, 4, 4, 7, 3, 6, 7, 1, 2]);

1.02037…