EXAMPLE  LIST Math Functions
This example describes how to generate random array (list) data and then to apply statistical functions specifically created for arrays.
Functions:
Item  Description 

LISTSUM Function  Computes the sum 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. 
LISTMIN Function  Computes the minimum 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. 
LISTMAX Function  Computes the maximum 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. 
LISTAVERAGE Function  Computes the average 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. 
LISTVAR Function  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. 
LISTSTDEV Function  Computes the standard deviation 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. 
LISTMODE Function  Computes the most common value 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. 
Also:
Item  Description 

RANGE Function  Computes an array of integers, from a beginning integer to an end (stop) integer, stepping by a third parameter. 
RAND Function  The 
ROUND Function  Rounds input value to the nearest integer. Input can be an Integer, a Decimal, a column reference, or an expression. Optional second argument can be used to specify the number of digits to which to round. 
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 


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 


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: x1 < x < x+4.
Transformation Name 


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 


Parameter: Columns  myArray1_0~myArray1_8 
Parameter: Formula  ROUND($col, 2) 
Renest these columns into an array:
Transformation Name 


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 


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 floatingpoint errors or additional digits in the results.
Sum of all values in the array (list):
Transformation Name 


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 


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 


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 


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 


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 


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 


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.