Computes the variance of all numeric values found in input array. Input can be an array literal, a column of arrays, or a function returning an array. Input values must be of Integer or Decimal type.

When this function is invoked, all of the values in the input array are passed to the corresponding columnar function. Some restrictions may apply. See VAR Function.

## Basic Usage

**Literal example:**

`listvar([0,0,2,4,6,8,10,12,14,16,18,20])`

**Output:** Returns the variance of all values in the literal array: `48.33333333`

.

**Column example:**

`listvar(myArray)`

**Output:** Returns the variance of all values in the arrays of the `myArray`

column.

## Syntax and Arguments

`listvar(array_ref)`

Argument | Required? | Data Type | Description |
---|---|---|---|

array_ref | Y | Array | Array literal, reference to column containing arrays, or function returning an array |

For more information on syntax standards, see Language Documentation Syntax Notes.

### array_ref

Reference to an array can be an array literal, function returning an array, or a single column containing arrays.

- If the input is not a valid numeric array, null values are returned.
- Non-numerical values within an input array are not factored in the computation.
- Multiple columns and wildcards are not supported.

**
Usage Notes:
**

Required? | Data Type | Example Value |
---|---|---|

Yes | Array | `myArray` |

## Examples

**Tip:** For additional examples, see Common Tasks.

### Example - Math functions for lists (arrays)

`LISTSUM`

- Sum all values in the array. See LISTSUM Function.`LISTMIN`

- Minimum value of all values in the array. See LISTMIN Function.`LISTMAX`

- Maximum value of all values in the array. See LISTMAX Function.`LISTAVERAGE`

- Average value of all values in the array. See LISTAVERAGE Function.`LISTVAR`

- Variance of all values in the array. See LISTVAR Function.`LISTSTDEV`

- Standard deviation of all values in the array. See LISTSTDEV Function.`LISTMODE`

- Most common value of all values in the array. See LISTMODE Function.

**Source:**

For this example, you can generate some randomized data using the following steps. First, you need to seed an array with a range of values using the RANGE function:

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `RANGE(5, 50, 5)` |

Parameter: New column name | `'myArray1'` |

Then, unpack this array, so you can add a random factor:

Transformation Name | `Unnest Objects into columns` |
---|---|

Parameter: Column | `myArray1` |

Parameter: Paths to elements | `'[0]', '[1]', '[2]', '[3]', '[4]', '[5]', '[6]', '[7]', '[8]', '[9]'` |

Parameter: Remove elements from original | `true` |

Parameter: Include original column name | `true` |

Add the randomizing factor. Here, you are adding randomization around individual values: x-1 < x < x+4.

Transformation Name | `Edit column with formula` |
---|---|

Parameter: Columns | `myArray1_0~myArray1_8` |

Parameter: Formula | `IF(RAND() > 0.5, $col + (5 * RAND()), $col - RAND())` |

To make the numbers easier to manipulate, you can round them to two decimal places:

Transformation Name | `Edit column with formula` |
---|---|

Parameter: Columns | `myArray1_0~myArray1_8` |

Parameter: Formula | `ROUND($col, 2)` |

Renest these columns into an array:

Transformation Name | `Nest columns into Objects` |
---|---|

Parameter: Columns | `myArray1_0, myArray1_1, myArray1_2, myArray1_3, myArray1_4, myArray1_5, myArray1_6, myArray1_7, myArray1_8` |

Parameter: Nest columns to | `Array` |

Parameter: New column name | `'myArray2'` |

Delete the unused columns:

Transformation Name | `Delete columns` |
---|---|

Parameter: Columns | `myArray1_0~myArray1_8,myArray1` |

Parameter: Action | `Delete selected columns` |

Your data should look similar to the following:

myArray2 |
---|

["8.29","9.63","14.63","19.63","24.63","29.63","34.63","39.63","44.63"] |

["8.32","14.01","19.01","24.01","29.01","34.01","39.01","44.01","49.01"] |

["4.55","9.58","14.58","19.58","24.58","29.58","34.58","39.58","44.58"] |

["9.22","14.84","19.84","24.84","29.84","34.84","39.84","44.84","49.84"] |

["8.75","13.36","18.36","23.36","28.36","33.36","38.36","43.36","48.36"] |

["8.47","14.76","19.76","24.76","29.76","34.76","39.76","44.76","49.76"] |

["4.93","9.99","14.99","19.99","24.99","29.99","34.99","39.99","44.99"] |

["4.65","14.98","19.98","24.98","29.98","34.98","39.98","44.98","49.98"] |

["7.80","14.62","19.62","24.62","29.62","34.62","39.62","44.62","49.62"] |

["9.32","9.96","14.96","19.96","24.96","29.96","34.96","39.96","44.96"] |

**Transformation:**

These steps demonstrate the individual math functions that you can apply to your list data without unnesting it:

**NOTE: **The NUMFORMAT function has been wrapped around each list function to account for any floating-point errors or additional digits in the results.

Sum of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTSUM(myArray2), '#.##')` |

Parameter: New column name | `'arraySum'` |

Minimum of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTMIN(myArray2), '#.##')` |

Parameter: New column name | `'arrayMin'` |

Maximum of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTMAX(myArray2), '#.##')` |

Parameter: New column name | `'arrayMax'` |

Average of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTAVERAGE(myArray2), '#.##')` |

Parameter: New column name | `'arrayAvg'` |

Variance of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTVAR(myArray2), '#.##')` |

Parameter: New column name | `'arrayVar'` |

Standard deviation of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTSTDEV(myArray2), '#.##')` |

Parameter: New column name | `'arrayStDv'` |

Mode (most common value) of all values in the array (list):

Transformation Name | `New formula` |
---|---|

Parameter: Formula type | `Single row formula` |

Parameter: Formula | `NUMFORMAT(LISTMODE(myArray2), '#.##')` |

Parameter: New column name | `'arrayMode'` |

**Results:**

Results for the first four math functions:

myArray2 | arrayAvg | arrayMax | arrayMin | arraySum |
---|---|---|---|---|

["8.29","9.63","14.63","19.63","24.63","29.63","34.63","39.63","44.63"] | 25.04 | 44.63 | 8.29 | 225.33 |

["8.32","14.01","19.01","24.01","29.01","34.01","39.01","44.01","49.01"] | 28.93 | 49.01 | 8.32 | 260.4 |

["4.55","9.58","14.58","19.58","24.58","29.58","34.58","39.58","44.58"] | 24.58 | 44.58 | 4.55 | 221.19 |

["9.22","14.84","19.84","24.84","29.84","34.84","39.84","44.84","49.84"] | 29.77 | 49.84 | 9.22 | 267.94 |

["8.75","13.36","18.36","23.36","28.36","33.36","38.36","43.36","48.36"] | 28.4 | 48.36 | 8.75 | 255.63 |

["8.47","14.76","19.76","24.76","29.76","34.76","39.76","44.76","49.76"] | 29.62 | 49.76 | 8.47 | 266.55 |

["4.93","9.99","14.99","19.99","24.99","29.99","34.99","39.99","44.99"] | 24.98 | 44.99 | 4.93 | 224.85 |

["4.65","14.98","19.98","24.98","29.98","34.98","39.98","44.98","49.98"] | 29.39 | 49.98 | 4.65 | 264.49 |

["7.80","14.62","19.62","24.62","29.62","34.62","39.62","44.62","49.62"] | 29.42 | 49.62 | 7.8 | 264.76 |

["9.32","9.96","14.96","19.96","24.96","29.96","34.96","39.96","44.96"] | 25.44 | 44.96 | 9.32 | 229 |

Results for the statistical functions:

myArray2 | arrayMode | arrayStDv | arrayVar |
---|---|---|---|

["8.29","9.63","14.63","19.63","24.63","29.63","34.63","39.63","44.63"] | 12.32 | 151.72 | |

["8.32","14.01","19.01","24.01","29.01","34.01","39.01","44.01","49.01"] | 13.03 | 169.78 | |

["4.55","9.58","14.58","19.58","24.58","29.58","34.58","39.58","44.58"] | 12.92 | 166.8 | |

["9.22","14.84","19.84","24.84","29.84","34.84","39.84","44.84","49.84"] | 13.02 | 169.46 | |

["8.75","13.36","18.36","23.36","28.36","33.36","38.36","43.36","48.36"] | 12.84 | 164.95 | |

["8.47","14.76","19.76","24.76","29.76","34.76","39.76","44.76","49.76"] | 13.14 | 172.56 | |

["4.93","9.99","14.99","19.99","24.99","29.99","34.99","39.99","44.99"] | 12.92 | 166.93 | |

["4.65","14.98","19.98","24.98","29.98","34.98","39.98","44.98","49.98"] | 13.9 | 193.16 | |

["7.80","14.62","19.62","24.62","29.62","34.62","39.62","44.62","49.62"] | 13.23 | 175.08 | |

["9.32","9.96","14.96","19.96","24.96","29.96","34.96","39.96","44.96"] | 12.21 | 149.17 |

Since all values are unique within an individual array, there is no most common value in any of them, which yields empty values for the `arrayMode`

column.

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