descriptive_statistics

defmodule DescriptiveStatistics do
  def sum ary do
    Enum.sum ary
  end

  def sort ary do
    Enum.sort ary
  end

  def max([]), do: nil
  def max ary do
    Enum.max ary
  end

  def min([]), do: nil
  def min ary do
    Enum.min ary
  end

  def length ary do
    Kernel.length ary
  end

  def mean([]), do: nil
  def mean ary do
    sum(ary) / __MODULE__.length(ary)
  end

  def median([]), do: nil
  def median ary do
    sorted = sort(ary)
    length = __MODULE__.length(ary)
    half   = div(length, 2)

    if(rem(length, 2) == 0) do
      mean([
        Enum.at(sorted, half - 1),
        Enum.at(sorted, half)
      ])
    else
      Enum.at(sorted, half)
    end
  end

  def variance([]), do: nil
  def variance ary do
    mean = mean(ary)
    sum(Enum.map(ary, &((mean - &1) * (mean - &1)))) /  __MODULE__.length(ary)
  end

  def standard_deviation([]), do: nil
  def standard_deviation(ary) do
    :math.sqrt(variance(ary))
  end

  def range([]), do: nil
  def range(ary) do
    sorted = sort(ary)
    List.last(sorted) - List.first(sorted)
  end

  def percentile_from_value([], _), do: nil
  def percentile_from_value(ary, value) do
    sorted = sort(ary)
    Enum.find_index(sorted, fn(x) -> x == value end) / __MODULE__.length(ary) * 100
    |> Float.ceil
    |> round
  end

  def value_from_percentile([], _), do: nil
  def value_from_percentile(ary, percentile) do
    idx = percentile / 100 * __MODULE__.length(ary)
      |> Float.ceil
      |> round
    ary
    |> sort
    |> Enum.fetch!(idx)
  end
end