### Statistics

Some more basic functions, this time focusing on sequences of numbers. First

`sum`

.
let sum t = (*http://en.wikipedia.org/wiki/Sum Summation is the operation of adding a sequence of numbers *) List.fold_left (fun acc x -> acc +. x) 0.0 tNow,

`arithmetic_mean`

follows trivially.
let arithmetic_mean t = (*http://en.wikipedia.org/wiki/Arithmetic_mean Simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection. *) (sum t)/.(float_of_int (List.length t))This formulation shows clearly the relationship between standard deviation and arithmetic mean.

let standard_deviation t = (*http://en.wikipedia.org/wiki/Standard_deviation For a finite set of numbers, the standard deviation is found by taking the square root of the average of the squared differences of the values from their average value. *) let av = arithmetic_mean t in let squared_diffs = List.fold_left (fun acc xi -> ((xi -. av) *. (xi -. av)) :: acc) [] t in sqrt (arithmetic_mean squared_diffs)The

`harmonic_mean`

function is, I find, a more interesting function.
let harmonic_mean t = (*http://en.wikipedia.org/wiki/Harmonic_mean The harmonic mean is the preferable method for averaging multiples, such as the price/earning ratio, in which price is in the numerator. If these ratios are averaged using an arithmetic mean (a common error), high data points are given greater weights than low data points. The harmonic mean, on the other hand, gives equal weight to each data point. *) let n = float_of_int (List.length t) in let denom=List.fold_left (fun acc xi -> acc +. 1.0 /. xi) 0.0 t in n /. denom

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