Excerpt 

This example describes how to generate random array (list) data and then to apply statistical functions specifically created for arrays. 
Functions:
D generate list excerpts 

pages  LISTSUM Function,LISTMIN Function,LISTMAX Function,LISTAVERAGE Function,LISTVAR Function,LISTSTDEV Function,LISTMODE Function 


Also:
D generate list excerpts 

pages  RANGE Function,RAND Function,ROUND 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:
D trans 

RawWrangle  true 

p03Value  'myArray1' 

Type  step 

WrangleText  derive type: single value: RANGE(5, 50, 5) as: 'myArray1' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  RANGE(5, 50, 5) 

p03Name  New column name 

SearchTerm  New formula 


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

RawWrangle  true 

p03Value  true 

Type  step 

WrangleText  unnest col: myArray1 keys: '[0]', '[1]', '[2]', '[3]', '[4]', '[5]', '[6]', '[7]', '[8]', '[9]' pluck: true markLineage: true 

p01Name  Column 

p01Value  myArray1 

p02Name  Paths to elements 

p02Value  '[0]', '[1]', '[2]', '[3]', '[4]', '[5]', '[6]', '[7]', '[8]', '[9]' 

p03Name  Remove elements from original 

p04Value  true 

p04Name  Include original column name 

SearchTerm  Unnest Objects into columns 


Add the randomizing factor. Here, you are adding randomization around individual values: x1 < x < x+4.
D trans 

RawWrangle  true 

Type  step 

WrangleText  set col: myArray1_0~myArray1_8 value: IF(RAND() > 0.5, $col + (5 * RAND()), $col  RAND()) 

p01Name  Columns 

p01Value  myArray1_0~myArray1_8 

p02Name  Formula 

p02Value  IF(RAND() > 0.5, $col + (5 * RAND()), $col  RAND()) 

SearchTerm  Edit column with formula 


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

RawWrangle  true 

Type  step 

WrangleText  set col: myArray1_0~myArray1_8 value: ROUND($col, 2) 

p01Name  Columns 

p01Value  myArray1_0~myArray1_8 

p02Name  Formula 

p02Value  ROUND($col, 2) 

SearchTerm  Edit column with formula 


Renest these columns into an array:
D trans 

RawWrangle  true 

p03Value  'myArray2' 

Type  step 

WrangleText  nest col: myArray1_0, myArray1_1, myArray1_2, myArray1_3, myArray1_4, myArray1_5, myArray1_6, myArray1_7, myArray1_8 into: array as: 'myArray2' 

p01Name  Columns 

p01Value  myArray1_0, myArray1_1, myArray1_2, myArray1_3, myArray1_4, myArray1_5, myArray1_6, myArray1_7, myArray1_8 

p02Name  Nest columns to 

p02Value  Array 

p03Name  New column name 

SearchTerm  Nest columns into Objects 


Delete the unused columns:
D trans 

RawWrangle  true 

Type  step 

WrangleText  drop col: myArray1_0~myArray1_8,myArray1 action: Drop 

p01Name  Columns 

p01Value  myArray1_0~myArray1_8,myArray1 

p02Name  Action 

p02Value  Delete selected columns 

SearchTerm  Delete 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:
Info 

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):
D trans 

RawWrangle  true 

p03Value  'arraySum' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTSUM(myArray2), '#.##') as: 'arraySum' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTSUM(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


Minimum of all values in the array (list):
D trans 

RawWrangle  true 

p03Value  'arrayMin' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTMIN(myArray2), '#.##') as: 'arrayMin' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTMIN(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


Maximum of all values in the array (list):
D trans 

RawWrangle  true 

p03Value  'arrayMax' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTMAX(myArray2), '#.##') as: 'arrayMax' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTMAX(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


Average of all values in the array (list):
D trans 

RawWrangle  true 

p03Value  'arrayAvg' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTAVERAGE(myArray2), '#.##') as: 'arrayAvg' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTAVERAGE(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


Variance of all values in the array (list):
D trans 

RawWrangle  true 

p03Value  'arrayVar' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTVAR(myArray2), '#.##') as: 'arrayVar' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTVAR(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


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

RawWrangle  true 

p03Value  'arrayStDv' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTSTDEV(myArray2), '#.##') as: 'arrayStDv' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTSTDEV(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


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

RawWrangle  true 

p03Value  'arrayMode' 

Type  step 

WrangleText  derive type: single value: NUMFORMAT(LISTMODE(myArray2), '#.##') as: 'arrayMode' 

p01Name  Formula type 

p01Value  Single row formula 

p02Name  Formula 

p02Value  NUMFORMAT(LISTMODE(myArray2), '#.##') 

p03Name  New column name 

SearchTerm  New formula 


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.
D s also 

label  example_list_math_functions 

