# Diversity prediction theorem

Diversity prediction theorem is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The wisdom of the crowd is the collective opinion of a group of individuals rather than that of a single expert.

Wisdom-of-the-crowds research routinely attributes the superiority of crowd averages over individual judgments to the elimination of individual noise, an explanation that assumes independence of the individual judgments from each other. Thus the crowd tends to make its best decisions if it is made up of diverse opinions and ideologies.

Scott E. Page introduced the diversity prediction theorem: "The squared error of the collective prediction equals the average squared error minus the predictive diversity". Therefore, when the diversity in a group is large, the error of the crowd is small.

- Average Individual Error: Average of the individual squared errors

- Collective Error: Squared error of the collective prediction

- Prediction Diversity: Average squared distance from the individual predictions to the collective prediction

So, The Diversity Prediction Theorem: Given a crowd of predictive models

Collective Error = Average Individual Error - Prediction Diversity

## 11l

Translation of: C++
`F average_square_diff(a, predictions)   R sum(predictions.map(x -> (x - @a) ^ 2)) / predictions.len F diversity_theorem(truth, predictions)   V average = sum(predictions) / predictions.len   print(‘average-error: ’average_square_diff(truth, predictions)"\n"‘’         ‘crowd-error:   ’((truth - average) ^ 2)"\n"‘’         ‘diversity:     ’average_square_diff(average, predictions)) diversity_theorem(49.0, [Float(48), 47, 51])diversity_theorem(49.0, [Float(48), 47, 51, 42])`
Output:
```average-error: 3
crowd-error:   0.111111111
diversity:     2.888888889
average-error: 14.5
crowd-error:   4
diversity:     10.5
```

## C

Accepts inputs from command line, prints out usage on incorrect invocation.

`  #include<string.h>#include<stdlib.h>#include<stdio.h> float mean(float* arr,int size){	int i = 0;	float sum = 0; 	while(i != size)		sum += arr[i++]; 	return sum/size;} float variance(float reference,float* arr, int size){	int i=0;	float* newArr = (float*)malloc(size*sizeof(float)); 	for(;i<size;i++)		newArr[i] = (reference - arr[i])*(reference - arr[i]); 	return mean(newArr,size);} float* extractData(char* str, int *len){	float* arr;	int i=0,count = 1;	char* token; 	while(str[i]!=00){		if(str[i++]==',')			count++;	} 	arr = (float*)malloc(count*sizeof(float));	*len = count; 	token = strtok(str,","); 	i = 0; 	while(token!=NULL){		arr[i++] = atof(token);		token = strtok(NULL,",");	} 	return arr;} int main(int argC,char* argV[]){	float* arr,reference,meanVal;	int len;	if(argC!=3)		printf("Usage : %s <reference value> <observations separated by commas>");	else{		arr = extractData(argV[2],&len); 		reference = atof(argV[1]); 		meanVal = mean(arr,len); 		printf("Average Error : %.9f\n",variance(reference,arr,len));		printf("Crowd Error : %.9f\n",(reference - meanVal)*(reference - meanVal));		printf("Diversity : %.9f",variance(meanVal,arr,len));	} 	return 0;} `

Invocation and Output :

```C:\rosettaCode>diversityTheorem.exe 49 48,47,51
Average Error : 3.000000000
Crowd Error : 0.111110263
Diversity : 2.888888597
C:\rosettaCode>diversityTheorem.exe 49 48,47,51,42
Average Error : 14.500000000
Crowd Error : 4.000000000
Diversity : 10.500000000
```

## C++

` #include <iostream>#include <vector>#include <numeric> float sum(const std::vector<float> &array){    return std::accumulate(array.begin(), array.end(), 0.0);} float square(float x){    return x * x;} float mean(const std::vector<float> &array){    return sum(array) / array.size();} float averageSquareDiff(float a, const std::vector<float> &predictions){    std::vector<float> results;    for (float x : predictions)        results.push_back(square(x - a));    return mean(results);} void diversityTheorem(float truth, const std::vector<float> &predictions){    float average = mean(predictions);    std::cout        << "average-error: " << averageSquareDiff(truth, predictions) << "\n"        << "crowd-error: " << square(truth - average) << "\n"        << "diversity: " << averageSquareDiff(average, predictions) << std::endl;} int main() {    diversityTheorem(49, {48,47,51});    diversityTheorem(49, {48,47,51,42});    return 0;} `
Output:
```average-error: 3
crowd-error: 0.11111
diversity: 2.88889
average-error: 14.5
crowd-error: 4
diversity: 10.5
```

## C#

` using System;using System.Linq;using System.Collections.Generic; public class MainClass {    static double Square(double x) => x * x;     static double AverageSquareDiff(double a, IEnumerable<double> predictions)        => predictions.Select(x => Square(x - a)).Average();     static void DiversityTheorem(double truth, IEnumerable<double> predictions)    {        var average = predictions.Average();        Console.WriteLine(\$@"average-error: {AverageSquareDiff(truth, predictions)}crowd-error: {Square(truth - average)}diversity: {AverageSquareDiff(average, predictions)}");    }     public static void Main() {	DiversityTheorem(49, new []{48d,47,51});    	DiversityTheorem(49, new []{48d,47,51,42});    }}`
Output:
```average-error: 3
crowd-error: 0.11111
diversity: 2.88889
average-error: 14.5
crowd-error: 4
diversity: 10.5
```

## Clojure

John Lawrence Aspden's code posted on Diversity Prediction Theorem.

` (defn diversity-theorem [truth predictions]  (let [square (fn[x] (* x x))        mean (/ (reduce + predictions) (count predictions))        avg-sq-diff (fn[a] (/ (reduce + (for [x predictions] (square (- x a)))) (count predictions)))]    {:average-error (avg-sq-diff truth)     :crowd-error (square (- truth mean))     :diversity (avg-sq-diff mean)})) (println (diversity-theorem 49 '(48 47 51)))(println (diversity-theorem 49 '(48 47 51 42))) `
Output:
```{:average-error 3, :crowd-error 1/9, :diversity 26/9}
{:average-error 29/2, :crowd-error 4, :diversity 21/2}
```

## Go

`package main import "fmt" func averageSquareDiff(f float64, preds []float64) (av float64) {    for _, pred := range preds {        av += (pred - f) * (pred - f)    }    av /= float64(len(preds))    return} func diversityTheorem(truth float64, preds []float64) (float64, float64, float64) {    av := 0.0    for _, pred := range preds {        av += pred    }    av /= float64(len(preds))    avErr := averageSquareDiff(truth, preds)    crowdErr := (truth - av) * (truth - av)    div := averageSquareDiff(av, preds)    return avErr, crowdErr, div} func main() {    predsArray := [2][]float64{{48, 47, 51}, {48, 47, 51, 42}}    truth := 49.0    for _, preds := range predsArray {        avErr, crowdErr, div := diversityTheorem(truth, preds)        fmt.Printf("Average-error : %6.3f\n", avErr)        fmt.Printf("Crowd-error   : %6.3f\n", crowdErr)        fmt.Printf("Diversity     : %6.3f\n\n", div)    }}`
Output:
```Average-error :  3.000
Crowd-error   :  0.111
Diversity     :  2.889

Average-error : 14.500
Crowd-error   :  4.000
Diversity     : 10.500
```

## JavaScript

### ES5

`'use strict'; function sum(array) {    return array.reduce(function (a, b) {        return a + b;    });} function square(x) {    return x * x;} function mean(array) {    return sum(array) / array.length;} function averageSquareDiff(a, predictions) {    return mean(predictions.map(function (x) {        return square(x - a);    }));} function diversityTheorem(truth, predictions) {    var average = mean(predictions);    return {        'average-error': averageSquareDiff(truth, predictions),        'crowd-error': square(truth - average),        'diversity': averageSquareDiff(average, predictions)    };} console.log(diversityTheorem(49, [48,47,51]))console.log(diversityTheorem(49, [48,47,51,42])) `
Output:
```{ 'average-error': 3,
'crowd-error': 0.11111111111111269,
diversity: 2.888888888888889 }
{ 'average-error': 14.5, 'crowd-error': 4, diversity: 10.5 }
```

### ES6

`(() => {    'use strict';     // mean :: Num a => [a] -> b    const mean = xs => {        const lng = xs.length;         return lng > 0 ? (            xs.reduce((a, b) => a + b, 0) / lng        ) : undefined;    }     // meanErrorSquared :: Num a => a -> [a] -> b    const meanErrorSquared = (observed, predictions) =>        mean(predictions.map(x => Math.pow(x - observed, 2)));      // diversityValues :: Num a => a -> [a] ->    //     {mean-Error :: b, crowd-error :: b, diversity :: b}    const diversityValues = (observed, predictions) => {        const predictionMean = mean(predictions);         return {            'mean-error': meanErrorSquared(observed, predictions),            'crowd-error': Math.pow(observed - predictionMean, 2),            'diversity': meanErrorSquared(predictionMean, predictions)        };    }      // TEST     // show :: a -> String    const show = x => JSON.stringify(x, null, 2);     return show([{        observed: 49,        predictions: [48, 47, 51]    }, {        observed: 49,        predictions: [48, 47, 51, 42]    }].map(x => {        const dctData = diversityValues(x.observed, x.predictions),            dct = {};         return (            Object.keys(dctData)            .forEach(k => dct[k] = dctData[k].toPrecision(3)),            dct        );    }));})();`
Output:
```[
{
"mean-error": "3.00",
"crowd-error": "0.111",
"diversity": "2.89"
},
{
"mean-error": "14.5",
"crowd-error": "4.00",
"diversity": "10.5"
}
]```

## Jsish

From Typescript entry.

`/* Diverisity Prediction Theorem, in Jsish */"use strict"; function sum(arr:array):number {    return arr.reduce(function(acc, cur, idx, arr) { return acc + cur; });} function square(x:number):number {    return x * x;} function mean(arr:array):number {    return sum(arr) / arr.length;} function averageSquareDiff(a:number, predictions:array):number {    return mean(predictions.map(function(x:number):number { return square(x - a); }));} function diversityTheorem(truth:number, predictions:array):object {    var average = mean(predictions);    return {        "average-error": averageSquareDiff(truth, predictions),        "crowd-error": square(truth - average),        "diversity": averageSquareDiff(average, predictions)    };} ;diversityTheorem(49, [48,47,51]);;diversityTheorem(49, [48,47,51,42]); /*=!EXPECTSTART!=diversityTheorem(49, [48,47,51]) ==> { "average-error":3, "crowd-error":0.1111111111111127, diversity:2.888888888888889 }diversityTheorem(49, [48,47,51,42]) ==> { "average-error":14.5, "crowd-error":4, diversity:10.5 }=!EXPECTEND!=*/`
Output:
```prompt\$ jsish -u diversityPrediction.jsi
[PASS] diversityPrediction.jsi```

## Julia

Works with: Julia version 0.6
`function diversitytheorem(truth::T, pred::Vector{T}) where T<:Number    avg = mean(pred)    avgerr = mean((pred .- truth) .^ 2)    crderr = (avg - truth) ^ 2    divers = mean((pred .- avg) .^ 2)    return avgerr, crderr, diversend for (t, s) in [(49, [48, 47, 51]),               (49, [48, 47, 51, 42])]    avgerr, crderr, divers = diversitytheorem(t, s)    println("""    average-error : \$avgerr    crowd-error   : \$crderr    diversity     : \$divers    """)end`
Output:
```average-error : 3.0
crowd-error   : 0.11111111111111269
diversity     : 2.888888888888889

average-error : 14.5
crowd-error   : 4.0
diversity     : 10.5
```

## Kotlin

Translation of: TypeScript
`// version 1.1.4-3 fun square(d: Double) = d * d fun averageSquareDiff(d: Double, predictions: DoubleArray) =     predictions.map { square(it - d) }.average() fun diversityTheorem(truth: Double, predictions: DoubleArray): String {    val average = predictions.average()    val f = "%6.3f"    return "average-error : \${f.format(averageSquareDiff(truth, predictions))}\n" +           "crowd-error   : \${f.format(square(truth - average))}\n" +           "diversity     : \${f.format(averageSquareDiff(average, predictions))}\n"} fun main(args: Array<String>) {    println(diversityTheorem(49.0, doubleArrayOf(48.0, 47.0, 51.0)))    println(diversityTheorem(49.0, doubleArrayOf(48.0, 47.0, 51.0, 42.0)))}`
Output:
```average-error :  3.000
crowd-error   :  0.111
diversity     :  2.889

average-error : 14.500
crowd-error   :  4.000
diversity     : 10.500
```

## Perl

`sub diversity {    my(\$truth, @pred) = @_;    my(\$ae,\$ce,\$cp,\$pd,\$stats);     \$cp += \$_/@pred for @pred;      # collective prediction    \$ae = avg_error(\$truth, @pred); # average individual error    \$ce = (\$cp - \$truth)**2;        # collective error    \$pd = avg_error(\$cp, @pred);    # prediction diversity     my \$fmt = "%13s: %6.3f\n";    \$stats  = sprintf \$fmt, 'average-error', \$ae;    \$stats .= sprintf \$fmt, 'crowd-error',   \$ce;    \$stats .= sprintf \$fmt, 'diversity',     \$pd;} sub avg_error {    my(\$m, @v) = @_;    my(\$avg_err);    \$avg_err += (\$_ - \$m)**2 for @v;    \$avg_err/@v;} print diversity(49, qw<48 47 51>) . "\n";print diversity(49, qw<48 47 51 42>);`
Output:
```average-error:  3.000
crowd-error:  0.111
diversity:  2.889

average-error: 14.500
crowd-error:  4.000
diversity: 10.500```

## Perl 6

`sub diversity-calc(\$truth, @pred) {    my \$ae = avg-error(\$truth, @pred); # average individual error    my \$cp = ([+] @pred)/[email protected]pred;       # collective prediction    my \$ce = (\$cp - \$truth)**2;        # collective error    my \$pd = avg-error(\$cp, @pred);    # prediction diversity    return \$ae, \$ce, \$pd;} sub avg-error (\$m, @v) { ([+] (@v X- \$m) X**2) / +@v } sub diversity-format (@stats) {    gather {        for <average-error crowd-error diversity> Z @stats -> (\$label,\$value) {            take \$label.fmt("%13s") ~ ':' ~ \$value.fmt("%7.3f");        }    }} .say for diversity-format diversity-calc(49, <48 47 51>);.say for diversity-format diversity-calc(49, <48 47 51 42>);`
Output:
```average-error:  3.000
crowd-error:  0.111
diversity:  2.889
average-error: 14.500
crowd-error:  4.000
diversity: 10.500
```

## Phix

`function mean(sequence s)    return sum(s)/length(s)end function function variance(sequence s, atom d)    return mean(sq_power(sq_sub(s,d),2))end function function diversity_theorem(atom reference, sequence observations)    atom average_error = variance(observations,reference),         average = mean(observations),         crowd_error = power(reference-average,2),         diversity = variance(observations,average)    return {{"average_error",average_error},            {"crowd_error",crowd_error},            {"diversity",diversity}}end function procedure test(atom reference, sequence observations)    sequence res = diversity_theorem(reference, observations)    for i=1 to length(res) do        printf(1," %14s : %g\n",res[i])    end forend proceduretest(49, {48, 47, 51})test(49, {48, 47, 51, 42})`
Output:
```  average_error : 3
crowd_error : 0.111111
diversity : 2.88889
average_error : 14.5
crowd_error : 4
diversity : 10.5
```

## Python

By composition of pure functions:

Works with: Python version 3.7
`'''Diversity prediction theorem''' from itertools import chainfrom functools import reduce  # main :: IO ()def main():    '''Observed value: 49,       prediction lists: various.    '''     print(unlines(map(        showDiversityValues(49),        [            [48, 47, 51],            [48, 47, 51, 42],            [50, '?', 50, {}, 50],  # Non-numeric values.            []                      # Missing predictions.        ]    )))    print(unlines(map(        showDiversityValues('49'),  # String in place of number.        [            [50, 50, 50],            [40, 35, 40],        ]    )))  # meanErrorSquared :: Num -> [Num] -> Numdef meanErrorSquared(x):    '''The mean of the squared differences       between the observed value x and       a non-empty list of predictions ps.    '''    return lambda ps: mean(list(map(        lambda y: pow(y - x, 2),        ps    )))  #  diversityValues :: Num a => a -> [a] ->#     {mean-Error :: a, crowd-error :: a, diversity :: a}def diversityValues(x):    '''The mean error, crowd error and       diversity, for a given observation x       and a non-empty list of predictions ps.    '''    def go(ps):        mp = mean(ps)        return {            'mean-error': meanErrorSquared(x)(ps),            'crowd-error': pow(x - mp, 2),            'diversity': meanErrorSquared(mp)(ps)        }    return lambda ps: go(ps)  # FORMATTING ---------------------------------------------- # showDiversityValues :: Num -> [Num] -> Either String Stringdef showDiversityValues(x):    '''Formatted string representation       of diversity values for a given       observation x and a non-empty       list of predictions p.    '''    def go(x, ps):        def showDict(dct):            w = 4 + max(map(len, dct.keys()))             def showKV(a, kv):                k, v = kv                return a + k.rjust(w, ' ') + (                    ' : ' + showPrecision(3)(v) + '\n'                )            return 'Predictions: ' + showList(ps) + ' ->\n' + (                reduce(showKV, dct.items(), '')            )         def showProblem(e):            return (                unlines(map(indent(1), e)) if (                    isinstance(e, list)                ) else indent(1)(repr(e))            ) + '\n'         return 'Observation:  ' + repr(x) + '\n' + (            either(showProblem)(showDict)(                bindLR(numLR(x))(                    lambda n: bindLR(numsLR(ps))(                        compose(Right)(diversityValues(n))                    )                )            )        )    return lambda ps: go(x, ps)  # GENERIC ------------------------------------------------- # Right :: b -> Either a bdef Right(x):    '''Constructor for a populated Either (option type) value'''    return {'type': 'Either', 'Left': None, 'Right': x}  # Left :: a -> Either a bdef Left(x):    '''Constructor for an empty Either (option type) value       with an associated string.'''    return {'type': 'Either', 'Right': None, 'Left': x}  # bindLR (>>=) :: Either a -> (a -> Either b) -> Either bdef bindLR(m):    '''Either monad injection operator.       Two computations sequentially composed,       with any value produced by the first       passed as an argument to the second.'''    return lambda mf: (        mf(m.get('Right')) if None is m.get('Left') else m    )  # compose (<<<) :: (b -> c) -> (a -> b) -> a -> cdef compose(g):    '''Right to left function composition.'''    return lambda f: lambda x: g(f(x))  # concatMap :: (a -> [b]) -> [a] -> [b]def concatMap(f):    '''Concatenated list over which a function has been mapped.       The list monad can be derived by using a function f which       wraps its output in a list,       (using an empty list to represent computational failure).'''    return lambda xs: list(        chain.from_iterable(            map(f, xs)        )    )  # either :: (a -> c) -> (b -> c) -> Either a b -> cdef either(fl):    '''The application of fl to e if e is a Left value,       or the application of fr to e if e is a Right value.'''    return lambda fr: lambda e: fl(e['Left']) if (        None is e['Right']    ) else fr(e['Right'])  # indent :: Int -> String -> Stringdef indent(n):    '''String indented by n multiples       of four spaces'''    return lambda s: (n * 4 * ' ') + s  # mean :: [Num] -> Floatdef mean(xs):    '''Arithmetic mean of a list       of numeric values.    '''    return sum(xs) / float(len(xs))  # numLR :: a -> Either String Numdef numLR(x):    '''Either Right x if x is a float or int,       or a Left explanatory message.'''    return Right(x) if (        isinstance(x, (float, int))    ) else Left('Expected number, saw: ' + str(type(x)) + ' ' + repr(x))  # numsLR :: [a] -> Either String [Num]def numsLR(xs):    '''Either Right xs if all xs are float or int,       or a Left explanatory message.'''    def go(ns):        ls, rs = partitionEithers(map(numLR, ns))        return Left(ls) if ls else Right(rs)    return bindLR(        Right(xs) if (            bool(xs) and isinstance(xs, list)        ) else Left(            'Expected a non-empty list, saw: ' + (                str(type(xs)) + ' ' + repr(xs)            )        )    )(go)  # partitionEithers :: [Either a b] -> ([a],[b])def partitionEithers(lrs):    '''A list of Either values partitioned into a tuple       of two lists, with all Left elements extracted       into the first list, and Right elements       extracted into the second list.    '''    def go(a, x):        ls, rs = a        r = x.get('Right')        return (ls + [x.get('Left')], rs) if None is r else (            ls, rs + [r]        )    return reduce(go, lrs, ([], []))  # showList :: [a] -> Stringdef showList(xs):    '''Compact string representation of a list'''    return '[' + ','.join(str(x) for x in xs) + ']'  # showPrecision Int -> Float -> Stringdef showPrecision(n):    '''A string showing a floating point number       at a given degree of precision.'''    return lambda x: str(round(x, n))  # unlines :: [String] -> Stringdef unlines(xs):    '''A single string derived by the intercalation       of a list of strings with the newline character.'''    return '\n'.join(xs)  # MAIN ---if __name__ == '__main__':    main()`
Output:
```Observation:  49
Predictions: [48,47,51] ->
mean-error : 3.0
crowd-error : 0.111
diversity : 2.889

Observation:  49
Predictions: [48,47,51,42] ->
mean-error : 14.5
crowd-error : 4.0
diversity : 10.5

Observation:  49
Expected number, saw: <class 'str'> '?'
Expected number, saw: <class 'dict'> {}

Observation:  49
"Expected a non-empty list, saw: <class 'list'> []"

Observation:  '49'
"Expected number, saw: <class 'str'> '49'"

Observation:  '49'
"Expected number, saw: <class 'str'> '49'"```

## REXX

### version 1

`/* REXX */Numeric Digits 20Call diversityTheorem 49,'48 47 51'Say '--------------------------------------'Call diversityTheorem 49,'48 47 51 42'Exit diversityTheorem:  Parse Arg truth,list  average=average(list)  Say 'average-error='averageSquareDiff(truth,list)  Say 'crowd-error='||(truth-average)**2  Say 'diversity='averageSquareDiff(average,list)  Return average: Procedure  Parse Arg list  res=0  Do i=1 To words(list)    res=res+word(list,i)  /* accumulate list elements */    End  Return res/words(list)  /* return the average */ averageSquareDiff: Procedure  Parse Arg a,list  res=0  Do i=1 To words(list)    x=word(list,i)    res=res+(x-a)**2      /* accumulate square of differences */    End  Return res/words(list)  /* return the average */`
Output:
```average-error=3
crowd-error=0.11111111111111111089
diversity=2.8888888888888888889
--------------------------------------
average-error=14.5
crowd-error=4
diversity=10.5```

### version 2

Uses greater precision, but limits the output to six decimal digits past the decimal point   (see the last comment in the program).

`/*REXX program calculates:   average error,   crowd error,   and   prediction diversity.*/numeric digits 50                                /*set precision at fifty decimal digits*/call diversity 49,     48  47  51                /*true value,  and  crowd predictions. */call diversity 49,     48  47  51  42            /*  "    "      "     "        "       */exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/avg:   \$=0;    do k=1  for #;   \$=\$ +  word(ests, k)             ;   end;       return \$/#avgSD: \$=0;    do j=1  for #;   \$=\$ + (word(ests, j) - arg(1))**2;   end;       return \$/#/*──────────────────────────────────────────────────────────────────────────────────────*/diversity: parse arg true, ests;  #=words(ests)  /*get args;  count number of estimates.*/           say '   the  true   value: '  true  copies('═', 20)  'crowd estimates: '   ests           avg\$= avg()                           /* [↓]  avgSD=avg of squared difference*/           say '   the average error: '     format( avgSD(true)    , , 6) / 1           say '   the  crowd  error: '     format( (true-avg\$)**2 , , 6) / 1           say 'prediction diversity: '     format( avgSD(avg\$)    , , 6) / 1;   say;  say           return                                /*only show up to 6───┘  decimal digits*/`
output   when using the default inputs:
```   the  true   value:  49 ════════════════════ crowd estimates:  48 47 51
the average error:  3
the  crowd  error:  0.111111
prediction diversity:  2.888889

the  true   value:  49 ════════════════════ crowd estimates:  48 47 51 42
the average error:  14.5
the  crowd  error:  4
prediction diversity:  10.5
```

## Sidef

Translation of: Perl 6
`func avg_error(m, v) {    v.map { (_ - m)**2 }.sum / v.len} func diversity_calc(truth, pred) {    var ae = avg_error(truth, pred)    var cp = pred.sum/pred.len    var ce = (cp - truth)**2    var pd = avg_error(cp, pred)    return [ae, ce, pd]} func diversity_format(stats) {    gather {        for t,v in (%w(average-error crowd-error diversity) ~Z stats) {            take(("%13s" % t) + ':' + ('%7.3f' % v))        }    }} diversity_format(diversity_calc(49, [48, 47, 51])).each{.say}diversity_format(diversity_calc(49, [48, 47, 51, 42])).each{.say}`
Output:
```average-error:  3.000
crowd-error:  0.111
diversity:  2.889
average-error: 14.500
crowd-error:  4.000
diversity: 10.500
```

## TypeScript

` function sum(array: Array<number>): number {    return array.reduce((a, b) => a + b)} function square(x : number) :number {    return x * x} function mean(array: Array<number>): number {    return sum(array) / array.length} function averageSquareDiff(a: number, predictions: Array<number>): number {    return mean(predictions.map(x => square(x - a)))} function diversityTheorem(truth: number, predictions: Array<number>): Object {    const average: number = mean(predictions)    return {        "average-error": averageSquareDiff(truth, predictions),        "crowd-error": square(truth - average),        "diversity": averageSquareDiff(average, predictions)    }} console.log(diversityTheorem(49, [48,47,51]))console.log(diversityTheorem(49, [48,47,51,42])) `
Output:
```{ 'average-error': 3,
'crowd-error': 0.11111111111111269,
diversity: 2.888888888888889 }
{ 'average-error': 14.5, 'crowd-error': 4, diversity: 10.5 }
```

## zkl

Translation of: Sidef
`fcn avgError(m,v){ v.apply('wrap(n){ (n - m).pow(2) }).sum(0.0)/v.len() } fcn diversityCalc(truth,pred){  //(Float,List of Float)   ae,cp := avgError(truth,pred), pred.sum(0.0)/pred.len();   ce,pd := (cp - truth).pow(2),  avgError(cp, pred);   return(ae,ce,pd)} fcn diversityFormat(stats){  // ( (averageError,crowdError,diversity) )   T("average-error","crowd-error","diversity").zip(stats)   .pump(String,Void.Xplode,"%13s :%7.3f\n".fmt)}`
`diversityCalc(49.0, T(48.0,47.0,51.0)) : diversityFormat(_).println();diversityCalc(49.0, T(48.0,47.0,51.0,42.0)) : diversityFormat(_).println();`
Output:
```average-error :  3.000
crowd-error :  0.111
diversity :  2.889

average-error : 14.500
crowd-error :  4.000
diversity : 10.500
```