| 1 |
|
| 2 |
|
| 3 | # Function variance
|
| 4 |
|
| 5 | Compute the variance of a matrix or a list with values.
|
| 6 | In case of a (multi dimensional) array or matrix, the variance over all
|
| 7 | elements will be calculated.
|
| 8 |
|
| 9 | Additionally, it is possible to compute the variance along the rows
|
| 10 | or columns of a matrix by specifying the dimension as the second argument.
|
| 11 |
|
| 12 | Optionally, the type of normalization can be specified as the final
|
| 13 | parameter. The parameter `normalization` can be one of the following values:
|
| 14 |
|
| 15 | - 'unbiased' (default) The sum of squared errors is divided by (n - 1)
|
| 16 | - 'uncorrected' The sum of squared errors is divided by n
|
| 17 | - 'biased' The sum of squared errors is divided by (n + 1)
|
| 18 |
|
| 19 |
|
| 20 | Note that older browser may not like the variable name `var`. In that
|
| 21 | case, the function can be called as `math['var'](...)` instead of
|
| 22 | `math.var(...)`.
|
| 23 |
|
| 24 |
|
| 25 | ## Syntax
|
| 26 |
|
| 27 | ```js
|
| 28 | math.variance(a, b, c, ...)
|
| 29 | math.variance(A)
|
| 30 | math.variance(A, normalization)
|
| 31 | math.variance(A, dimension)
|
| 32 | math.variance(A, dimension, normalization)
|
| 33 | ```
|
| 34 |
|
| 35 | ### Parameters
|
| 36 |
|
| 37 | Parameter | Type | Description
|
| 38 | --------- | ---- | -----------
|
| 39 | `array` | Array | Matrix | A single matrix or or multiple scalar values
|
| 40 | `normalization` | string | Determines how to normalize the variance. Choose 'unbiased' (default), 'uncorrected', or 'biased'. Default value: 'unbiased'.
|
| 41 |
|
| 42 | ### Returns
|
| 43 |
|
| 44 | Type | Description
|
| 45 | ---- | -----------
|
| 46 | * | The variance
|
| 47 |
|
| 48 |
|
| 49 | ## Examples
|
| 50 |
|
| 51 | ```js
|
| 52 | math.variance(2, 4, 6) // returns 4
|
| 53 | math.variance([2, 4, 6, 8]) // returns 6.666666666666667
|
| 54 | math.variance([2, 4, 6, 8], 'uncorrected') // returns 5
|
| 55 | math.variance([2, 4, 6, 8], 'biased') // returns 4
|
| 56 |
|
| 57 | math.variance([[1, 2, 3], [4, 5, 6]]) // returns 3.5
|
| 58 | math.variance([[1, 2, 3], [4, 6, 8]], 0) // returns [4.5, 8, 12.5]
|
| 59 | math.variance([[1, 2, 3], [4, 6, 8]], 1) // returns [1, 4]
|
| 60 | math.variance([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.5, 2]
|
| 61 | ```
|
| 62 |
|
| 63 |
|
| 64 | ## See also
|
| 65 |
|
| 66 | [mean](mean.md),
|
| 67 | [median](median.md),
|
| 68 | [max](max.md),
|
| 69 | [min](min.md),
|
| 70 | [prod](prod.md),
|
| 71 | [std](std.md),
|
| 72 | [sum](sum.md)
|