Help › Functions
mean stdev Stdev max min hist histogram var Var median mode gmean hmean skew kurt cvar corr
mean(A, …) As in MathcadThe average of all the elements.
Takes numbers, vectors and matrices, any mix, and averages every element. See also stdev, var and median.
The answer is in the units of the first element.
stdev(A, …) As in MathcadThe population standard deviation of all the elements: the root of the mean squared distance from the mean.
Divides by n, the number of elements. Stdev divides by n − 1 instead, for a sample. See also mean.
The answer is in the units of the first element.
Stdev(A, …) As in MathcadThe sample standard deviation of all the elements: divides by n − 1.
Use it when the elements are a sample of something larger. stdev divides by n, for the whole population, and so is a little smaller. One element alone gives NaN, as 0 divided by 0.
The answer is in the units of the first element.
max(A, …) As in MathcadThe largest element.
Takes numbers, vectors and matrices, any mix. See also min.
The elements must be in compatible units; the answer keeps them.
min(A, …) As in MathcadThe smallest element.
Takes numbers, vectors and matrices, any mix. See also max.
The elements must be in compatible units; the answer keeps them.
hist(bounds, data) As in MathcadA vector of counts: how many data values fall in each interval between consecutive bounds.
bounds is a vector in rising order. Interval i holds the values above bounds[i] up to and including bounds[i+1], so a value on a boundary counts in the interval to its left. Values outside all the intervals are not counted. The answer has one fewer elements than bounds. histogram picks equal intervals for you.
histogram(n, data) As in MathcadA histogram with n equal intervals spanning the data: a matrix whose first column is each interval's midpoint and second its count.
The intervals run from the smallest value to the largest, and the smallest value counts in the first. A value on a boundary counts in the interval to its left. For intervals you choose, use hist. The two columns plot directly against each other.
The midpoints take the data's units; the counts have none.
var(A, …) As in MathcadThe variance of all the elements, dividing by their number n: the population variance.
Var divides by n − 1, for a sample. Takes numbers, vectors and matrices, any mix. Its square root is stdev.
In the square of the elements' units.
Var(A, …) As in MathcadThe sample variance of all the elements, dividing by n − 1.
var divides by n. Its square root is Stdev.
In the square of the elements' units.
median(A, …) As in MathcadThe middle value of all the elements, or the mean of the middle two when there's an even number.
In the elements' units.
mode(A, …) As in MathcadThe value that appears most often among all the elements.
gmean(A, …) As in MathcadThe geometric mean of all the elements: the nth root of their product.
hmean(A, …) As in MathcadThe harmonic mean of all the elements: n over the sum of their reciprocals.
skew(A, …) As in MathcadThe sample skewness of all the elements: how lopsided they are, positive when the long tail is above the mean.
n/((n − 1)(n − 2))·Σ((x − mean)/s)³, with s the sample standard deviation, as in Mathcad.
kurt(A, …) As in MathcadThe sample kurtosis of all the elements, in excess of a normal distribution's: positive for heavy tails.
Mathcad's formula, with the sample standard deviation and the n − 1, n − 2, n − 3 corrections.
cvar(A, B) As in MathcadThe covariance of two arrays of the same size, dividing by n.
Elements pair up by position. cvar(A, A) is var(A).
In the product of the two arrays' units.
corr(A, B) As in MathcadThe correlation of two arrays of the same size: from −1 to 1, 1 when one rises in step with the other.