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Variance of a data sample

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.


stats::variance(x1, x2, …, <Sample | Population>)
stats::variance([x1, x2, …], <Sample | Population>)
stats::variance(s, <c>, <Sample | Population>)


stats::variance( x1, x2, ..., xn) returns the variance


where is the arithmetic mean of the data xi.

stats::variance( x1, x2, ..., xn, Population) returns


The variance is the square of the standard deviation.

The column index c is optional, if the data are given by a stats::sample object containing only one non-string column. Cf. Example 3.

External statistical data stored in an ASCII file can be imported into a MuPAD® session via import::readdata. In particular, see Example 1 of the corresponding help page.


Example 1

We calculate the variance of three values:

stats::variance(2, 3, 5)

Alternatively, the data may be passed as a list:

stats::variance([2, 3, 5])

Example 2

We create a sample:

stats::sample([[a1, b1, c1], [a2, b2, c2]])
a1  b1  c1
a2  b2  c2

The variance of the second column is:

expand(stats::variance(%, 2))

Example 3

We create a sample consisting of one string column and one non-string column:

stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])
"1996"  1242
"1997"  1353
"1998"  1142

We compute the variance of the second column. In this case this column does not have to be specified, since it is the only non-string column:


We repeat the computation with the option Population:

float(stats::variance(%2, Population))


x1, x2, …

The statistical data: arithmetical expressions


A sample of domain type stats::sample


An integer representing a column index of the sample s. This column provides the data x1, x2, ….


Population, Sample

With Sample, the data are regarded as a “sample”, not as a full population. The default is Sample.

Return Values

Arithmetical expression.

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