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stat.js
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/* TODO(csilvers): fix these lint errors (http://eslint.org/docs/rules): */
/* eslint-disable camelcase, comma-dangle, indent, max-len, no-redeclare, no-var, one-var */
/* To fix, remove an entry above, run ka-lint, and fix errors. */
define(function(require) {
require("./math.js");
$.extend(KhanUtil, {
sum: function(values) {
var sum = 0;
$.each(values, function(index, value) {
sum += value;
});
return sum;
},
mean: function(values) {
return KhanUtil.sum(values) / values.length;
},
median: function(values) {
var sortedInts, median;
sortedInts = KhanUtil.sortNumbers(values);
if (values.length % 2 === 0) {
median = KhanUtil.roundTo(1,
(sortedInts[(values.length / 2) - 1] + sortedInts[values.length / 2]) / 2);
} else {
median = sortedInts[Math.floor(values.length / 2)];
}
return median;
},
mode: function(values) {
var numInstances = [];
var modeInstances = -1;
var mode;
for (var i = 0; i < values.length; i++) {
if (!numInstances[values[i]]) {
numInstances[values[i]] = 1;
} else {
numInstances[values[i]] += 1;
if (numInstances[values[i]] > modeInstances) {
modeInstances = numInstances[values[i]];
mode = values[i];
}
}
}
// iterate again to check for 'no mode'
for (var i = 0; i < numInstances.length; i++) {
if (numInstances[i]) {
if (i !== mode && numInstances[i] >= modeInstances) {
return false;
}
}
}
return mode;
},
variance: function(values) {
var xbar = KhanUtil.mean(values);
var n = values.length;
var sum = 0;
$.each(values, function(i, x_i) {
sum += (x_i - xbar) * (x_i - xbar);
});
return sum / (n - 1);
},
variancePop: function(values) {
var xbar = KhanUtil.mean(values);
var N = values.length;
var sum = 0;
$.each(values, function(i, x_i) {
sum += (x_i - xbar) * (x_i - xbar);
});
return sum / N;
},
stdDev: function(values) {
return Math.sqrt(KhanUtil.variance(values));
},
stdDevPop: function(values) {
return Math.sqrt(KhanUtil.variancePop(values));
},
// Gaussian distribution using Box-Muller transform
// defaults to standard normal unless target mean and stddev are passed
// Pass "count" to get an array of data
randGaussian: function(tgtMean, tgtStdDev, count) {
if (count == null) {
var x1, x2, rad;
do {
x1 = 2 * KhanUtil.random() - 1;
x2 = 2 * KhanUtil.random() - 1;
rad = x1 * x1 + x2 * x2;
} while (rad >= 1 || rad === 0);
var c = Math.sqrt(-2 * Math.log(rad) / rad);
return x1 * c * (tgtStdDev || 1) + (tgtMean || 0);
} else {
return $.map(new Array(count), function() {
return KhanUtil.randGaussian(tgtMean, tgtStdDev);
});
}
},
gaussianPDF: function(mean, stddev, x) {
return (1 / Math.sqrt(2 * Math.PI * stddev * stddev)) * Math.exp(-((x - mean) * (x - mean)) / (2 * stddev * stddev));
},
zScores: function(z) {
return ({
"0": 0.5, "1": 0.504, "2": 0.508, "3": 0.512, "4": 0.516,
"5": 0.5199, "6": 0.5239, "7": 0.5279, "8": 0.5319, "9": 0.5359,
"10": 0.5398, "11": 0.5438, "12": 0.5478, "13": 0.5517, "14": 0.5557,
"15": 0.5596, "16": 0.5636, "17": 0.5675, "18": 0.5714, "19": 0.5753,
"20": 0.5793, "21": 0.5832, "22": 0.5871, "23": 0.591, "24": 0.5948,
"25": 0.5987, "26": 0.6026, "27": 0.6064, "28": 0.6103, "29": 0.6141,
"30": 0.6179, "31": 0.6217, "32": 0.6255, "33": 0.6293, "34": 0.6331,
"35": 0.6368, "36": 0.6406, "37": 0.6443, "38": 0.648, "39": 0.6517,
"40": 0.6554, "41": 0.6591, "42": 0.6628, "43": 0.6664, "44": 0.67,
"45": 0.6736, "46": 0.6772, "47": 0.6808, "48": 0.6844, "49": 0.6879,
"50": 0.6915, "51": 0.695, "52": 0.6985, "53": 0.7019, "54": 0.7054,
"55": 0.7088, "56": 0.7123, "57": 0.7157, "58": 0.719, "59": 0.7224,
"60": 0.7257, "61": 0.7291, "62": 0.7324, "63": 0.7357, "64": 0.7389,
"65": 0.7422, "66": 0.7454, "67": 0.7486, "68": 0.7517, "69": 0.7549,
"70": 0.758, "71": 0.7611, "72": 0.7642, "73": 0.7673, "74": 0.7704,
"75": 0.7734, "76": 0.7764, "77": 0.7794, "78": 0.7823, "79": 0.7852,
"80": 0.7881, "81": 0.791, "82": 0.7939, "83": 0.7967, "84": 0.7995,
"85": 0.8023, "86": 0.8051, "87": 0.8078, "88": 0.8106, "89": 0.8133,
"90": 0.8159, "91": 0.8186, "92": 0.8212, "93": 0.8238, "94": 0.8264,
"95": 0.8289, "96": 0.8315, "97": 0.834, "98": 0.8365, "99": 0.8389,
"100": 0.8413, "101": 0.8438, "102": 0.8461, "103": 0.8485, "104": 0.8508,
"105": 0.8531, "106": 0.8554, "107": 0.8577, "108": 0.8599, "109": 0.8621,
"110": 0.8643, "111": 0.8665, "112": 0.8686, "113": 0.8708, "114": 0.8729,
"115": 0.8749, "116": 0.877, "117": 0.879, "118": 0.881, "119": 0.883,
"120": 0.8849, "121": 0.8869, "122": 0.8888, "123": 0.8907, "124": 0.8925,
"125": 0.8944, "126": 0.8962, "127": 0.898, "128": 0.8997, "129": 0.9015,
"130": 0.9032, "131": 0.9049, "132": 0.9066, "133": 0.9082, "134": 0.9099,
"135": 0.9115, "136": 0.9131, "137": 0.9147, "138": 0.9162, "139": 0.9177,
"140": 0.9192, "141": 0.9207, "142": 0.9222, "143": 0.9236, "144": 0.9251,
"145": 0.9265, "146": 0.9279, "147": 0.9292, "148": 0.9306, "149": 0.9319,
"150": 0.9332, "151": 0.9345, "152": 0.9357, "153": 0.937, "154": 0.9382,
"155": 0.9394, "156": 0.9406, "157": 0.9418, "158": 0.9429, "159": 0.9441,
"160": 0.9452, "161": 0.9463, "162": 0.9474, "163": 0.9484, "164": 0.9495,
"165": 0.9505, "166": 0.9515, "167": 0.9525, "168": 0.9535, "169": 0.9545,
"170": 0.9554, "171": 0.9564, "172": 0.9573, "173": 0.9582, "174": 0.9591,
"175": 0.9599, "176": 0.9608, "177": 0.9616, "178": 0.9625, "179": 0.9633,
"180": 0.9641, "181": 0.9649, "182": 0.9656, "183": 0.9664, "184": 0.9671,
"185": 0.9678, "186": 0.9686, "187": 0.9693, "188": 0.9699, "189": 0.9706,
"190": 0.9713, "191": 0.9719, "192": 0.9726, "193": 0.9732, "194": 0.9738,
"195": 0.9744, "196": 0.975, "197": 0.9756, "198": 0.9761, "199": 0.9767,
"200": 0.9772, "201": 0.9778, "202": 0.9783, "203": 0.9788, "204": 0.9793,
"205": 0.9798, "206": 0.9803, "207": 0.9808, "208": 0.9812, "209": 0.9817,
"210": 0.9821, "211": 0.9826, "212": 0.983, "213": 0.9834, "214": 0.9838,
"215": 0.9842, "216": 0.9846, "217": 0.985, "218": 0.9854, "219": 0.9857,
"220": 0.9861, "221": 0.9864, "222": 0.9868, "223": 0.9871, "224": 0.9875,
"225": 0.9878, "226": 0.9881, "227": 0.9884, "228": 0.9887, "229": 0.989,
"230": 0.9893, "231": 0.9896, "232": 0.9898, "233": 0.9901, "234": 0.9904,
"235": 0.9906, "236": 0.9909, "237": 0.9911, "238": 0.9913, "239": 0.9916,
"240": 0.9918, "241": 0.992, "242": 0.9922, "243": 0.9925, "244": 0.9927,
"245": 0.9929, "246": 0.9931, "247": 0.9932, "248": 0.9934, "249": 0.9936,
"250": 0.9938, "251": 0.994, "252": 0.9941, "253": 0.9943, "254": 0.9945,
"255": 0.9946, "256": 0.9948, "257": 0.9949, "258": 0.9951, "259": 0.9952,
"260": 0.9953, "261": 0.9955, "262": 0.9956, "263": 0.9957, "264": 0.9959,
"265": 0.996, "266": 0.9961, "267": 0.9962, "268": 0.9963, "269": 0.9964,
"270": 0.9965, "271": 0.9966, "272": 0.9967, "273": 0.9968, "274": 0.9969,
"275": 0.997, "276": 0.9971, "277": 0.9972, "278": 0.9973, "279": 0.9974,
"280": 0.9974, "281": 0.9975, "282": 0.9976, "283": 0.9977, "284": 0.9977,
"285": 0.9978, "286": 0.9979, "287": 0.9979, "288": 0.998, "289": 0.9981,
"290": 0.9981, "291": 0.9982, "292": 0.9982, "293": 0.9983, "294": 0.9984,
"295": 0.9984, "296": 0.9985, "297": 0.9985, "298": 0.9986, "299": 0.9986,
"300": 0.9987, "301": 0.9987, "302": 0.9987, "303": 0.9988, "304": 0.9988,
"305": 0.9989, "306": 0.9989, "307": 0.9989, "308": 0.999, "309": 0.999
}[z]);
}
});
});