normal distribution thrown into scores from 0 - 100

gistfile1.txt

var scores = [0,2,3,2,24,24,2,2];


//get the mean
var avg = 0;
scores.forEach(function(a) {
  avg+= a;
});
avg = avg / scores.length;

//get the standard_deviation
var devs = 0;
scores.forEach(function(a) {
  devs += Math.pow(avg-a,2);
});
var standard_deviation = Math.sqrt(devs/(scores.length-1));


//normal distribution function
var normal = function(num) {
  return (1/(standard_deviation * Math.sqrt(2*Math.PI))) *
    Math.exp(-(Math.pow(num-avg,2)) / (2 * (Math.pow(standard_deviation,2))));
}

//calculate the size of integral
var integral = 0;
var bar_width = standard_deviation/100;
for (var a=1; a<400; a++) {
  integral += bar_width*normal(a*bar_width);
}
integral = integral*2;


//make the mappings from 0-100 based on the proportion of the integral
var mapping = {};
var start = integral/2;
for (var a=1; a<400; a++) {
  var proportion = Math.floor(100*(bar_width*normal(a*bar_width)+start/integral));
  if (!mapping[proportion]) { mapping[proportion] = a*bar_width };
  start += bar_width*normal(a*bar_width);
}

//bucket divisions
var divisions = {};
for (var a in mapping) {
  if (a == 50) { divisions[avg] = 50  }
  else {
    divisions[avg+mapping[a]] = parseInt(a);
    divisions[avg-mapping[a]] = 50-(a-50);
  }
}


var buckets= {};
//now put them into buckets of 0-100
var testsum = 0;
scores.forEach(function(a) {
  var closest = 100000;
  var bucket = 0;
  for (var d in divisions) {
    if (closest > Math.abs(a-d)) {
      bucket = divisions[d]
      closest = Math.abs(a-d);
    }
  }

  console.log(a, bucket);


});