I am trying to calculate Z-scores using PHP. Essentially, I am looking for the most efficient way to calculate the mean and standard deviation of a data set (PHP array). Any suggestions on how to do this in PHP?
I am trying to do this in the smallest number of steps.
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.
To calculate the standard deviation, we have to first calculate the variance. The variance can be calculated as the sum of squares of differences between all numbers and means. Finally to get the standard deviation we will use the formula, √(variance/no_of_elements).
Key Takeaways. Standard deviation defines the line along which a particular data point lies. Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.
If you know the mean you know the standard deviation. Take your data point, subtract the mean from the data point and then divide by your standard deviation. That gives you your Z-score.
to calculate the mean you can do:
$mean = array_sum($array)/count($array)
standard deviation is like so:
// Function to calculate square of value - mean
function sd_square($x, $mean) { return pow($x - $mean,2); }
// Function to calculate standard deviation (uses sd_square)
function sd($array) {
// square root of sum of squares devided by N-1
return sqrt(array_sum(array_map("sd_square", $array, array_fill(0,count($array), (array_sum($array) / count($array)) ) ) ) / (count($array)-1) );
}
right off this page
How about using the built in statistics package like stats_standard_deviation and stats_harmonic_mean. I can't find a function for standard means, but if you know anything about statistics, I'm sure you can figure something out using the built-in functions.
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