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August 29, 2015 13:56
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Translates a list of numbers assumed to be distributed normally to another normal distribution with the required mean and standard deviation.
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| function redistribute(numbers, new_mean, new_std_deviation) { | |
| // compute the mean of the list of numbers | |
| // μ = (Σ x_i) / n | |
| var sum = 0; | |
| numbers.forEach(function (i) {sum += i}); | |
| var mean = sum / numbers.length; | |
| // compute the std deviation of the numbers: | |
| // σ = √(Σ (x_i - μ)² / n) | |
| sum = 0; | |
| numbers.forEach(function (i) {sum += Math.pow(i - mean, 2)}); | |
| var std_dev = Math.sqrt(sum / numbers.length); | |
| var res = []; | |
| numbers.forEach(function (i) { | |
| // Move number to a standar normal distribution (µ = 0, σ = 1) | |
| // x' = (x - µ) / σ | |
| var normal = (i - mean) / std_dev; | |
| // now move it to its new position | |
| // x'' = (x * σ') + µ' | |
| res.push((normal * new_std_deviation) + new_mean); | |
| }); | |
| return res; | |
| } | |
| var grades = [2.5, 3.1, 1.7, 2.2, 3.0, 2.6, 2.7, 1.9, 2.1]; | |
| // The new grades will have an average of 3.5 | |
| // and the 68 % of the grades will be between 3.0 and 4.0 | |
| var new_grades = redistribute(grades, 3.5, 0.5); | |
| // new_grades = [3.59, 4.25, 2.70, 3.25, 4.14, 3.69, 3.80, 2.92, 3.14] |
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